<?xml version="1.0" encoding="us-ascii"?>
<!--XBRL document created with Toppan Merrill Bridge  9.6.7401.38943 -->
<!--Based on XBRL 2.1-->
<!--Created on: 5/6/2020 11:05:54 AM-->
<!--Modified on: 5/6/2020 11:05:54 AM-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:xlink="http://www.w3.org/1999/xlink" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#StatementCondensedConsolidatedBalanceSheets" roleURI="http://www.papajohns.com/role/StatementCondensedConsolidatedBalanceSheets" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#StatementCondensedConsolidatedStatementsOfOperations" roleURI="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#StatementCondensedConsolidatedStatementsOfComprehensiveLoss" roleURI="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfComprehensiveLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#StatementCondensedConsolidatedStatementsOfStockholdersDeficit" roleURI="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfStockholdersDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#StatementCondensedConsolidatedStatementsOfCashFlows" roleURI="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfCashFlows" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#DisclosureUpdateToSignificantAccountingPoliciesNoncontrollingInterestAndJointVenturesDetails" roleURI="http://www.papajohns.com/role/DisclosureUpdateToSignificantAccountingPoliciesNoncontrollingInterestAndJointVenturesDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#DisclosureRevenueRecognitionTransactionPriceAllocatedToRemainingPerformanceObligationsDetails" roleURI="http://www.papajohns.com/role/DisclosureRevenueRecognitionTransactionPriceAllocatedToRemainingPerformanceObligationsDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#DisclosureCommonStockAndSeriesBConvertiblePreferredStockCashDividendDetails" roleURI="http://www.papajohns.com/role/DisclosureCommonStockAndSeriesBConvertiblePreferredStockCashDividendDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#DisclosureEarningsLossPerShareDetails" roleURI="http://www.papajohns.com/role/DisclosureEarningsLossPerShareDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#DisclosureOtherGeneralExpensesIncomeDetails" roleURI="http://www.papajohns.com/role/DisclosureOtherGeneralExpensesIncomeDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="pzza-20200506.xsd#DisclosureSegmentInformationScheduleOfSegmentReportingInformationBySegmentDetails" roleURI="http://www.papajohns.com/role/DisclosureSegmentInformationScheduleOfSegmentReportingInformationBySegmentDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <calculationLink xlink:role="http://www.papajohns.com/role/StatementCondensedConsolidatedBalanceSheets" xlink:type="extended" xlink:title="00100 - Statement - Condensed Consolidated Balance Sheets" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent_637243599506436522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_AssetsCurrent_637243599506436522" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_637243599506436522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_637243599506436522" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent_637243599506436522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_AccountsReceivableNetCurrent_637243599506436522" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NotesAndLoansReceivableNetCurrent" xlink:label="us-gaap_NotesAndLoansReceivableNetCurrent_637243599506436522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_NotesAndLoansReceivableNetCurrent_637243599506436522" order="3" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncomeTaxReceivable" xlink:label="us-gaap_IncomeTaxReceivable_637243599506436522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_IncomeTaxReceivable_637243599506436522" order="4" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_InventoryNet" xlink:label="us-gaap_InventoryNet_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_InventoryNet_637243599506446522" order="5" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_637243599506446522" order="6" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PrepaidExpenseCurrent" xlink:label="us-gaap_PrepaidExpenseCurrent_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent_637243599506436522" xlink:to="us-gaap_PrepaidExpenseCurrent_637243599506446522" order="7" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_637243599506446522" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_FinanceLeaseRightOfUseAsset" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_FinanceLeaseRightOfUseAsset_637243599506446522" order="3" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_637243599506446522" order="4" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NotesAndLoansReceivableNetNoncurrent" xlink:label="us-gaap_NotesAndLoansReceivableNetNoncurrent_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_NotesAndLoansReceivableNetNoncurrent_637243599506446522" order="5" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_Goodwill" xlink:label="us-gaap_Goodwill_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Goodwill_637243599506446522" order="6" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_DeferredIncomeTaxAssetsNet" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_637243599506446522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_DeferredIncomeTaxAssetsNet_637243599506446522" order="7" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherAssetsNoncurrent" xlink:label="us-gaap_OtherAssetsNoncurrent_637243599506456525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OtherAssetsNoncurrent_637243599506456525" order="8" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities_637243599506456525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_Liabilities_637243599506456525" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent_637243599506456525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_LiabilitiesCurrent_637243599506456525" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ContractWithCustomerLiabilityCurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_637243599506456525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_ContractWithCustomerLiabilityCurrent_637243599506456525" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_FinanceLeaseLiabilityCurrent" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_637243599506456525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent_637243599506456525" order="2" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_637243599506456525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_637243599506456525" order="3" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_LongTermDebtCurrent" xlink:label="us-gaap_LongTermDebtCurrent_637243599506466523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_LongTermDebtCurrent_637243599506466523" order="4" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent_637243599506466523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_AccountsPayableCurrent_637243599506466523" order="5" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_TaxesPayableCurrent" xlink:label="us-gaap_TaxesPayableCurrent_637243599506466523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_TaxesPayableCurrent_637243599506466523" order="6" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_637243599506466523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent_637243599506456525" xlink:to="us-gaap_AccruedLiabilitiesAndOtherLiabilities_637243599506466523" order="7" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityNoncurrent_637243599506466523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_ContractWithCustomerLiabilityNoncurrent_637243599506466523" order="2" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_637243599506466523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent_637243599506466523" order="3" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_637243599506476522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_637243599506476522" order="4" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_LongTermDebtNoncurrent" xlink:label="us-gaap_LongTermDebtNoncurrent_637243599506476522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_LongTermDebtNoncurrent_637243599506476522" order="5" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_637243599506476522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_DeferredIncomeTaxLiabilitiesNet_637243599506476522" order="6" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherLiabilitiesNoncurrent" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_637243599506476522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities_637243599506456525" xlink:to="us-gaap_OtherLiabilitiesNoncurrent_637243599506476522" order="7" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_637243599506476522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_637243599506476522" order="2" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_637243599506476522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_637243599506476522" order="3" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_637243599506486523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_637243599506486523" order="4" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity_637243599506486523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_637243599506486523" xlink:to="us-gaap_StockholdersEquity_637243599506486523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue_637243599506486523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity_637243599506486523" xlink:to="us-gaap_CommonStockValue_637243599506486523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital_637243599506486523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity_637243599506486523" xlink:to="us-gaap_AdditionalPaidInCapital_637243599506486523" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_637243599506486523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity_637243599506486523" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_637243599506486523" order="3" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_637243599506496522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity_637243599506486523" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_637243599506496522" order="4" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_TreasuryStockValue" xlink:label="us-gaap_TreasuryStockValue_637243599506496522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity_637243599506486523" xlink:to="us-gaap_TreasuryStockValue_637243599506496522" order="5" use="optional" weight="-1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_MinorityInterest" xlink:label="us-gaap_MinorityInterest_637243599506496522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_637243599506486523" xlink:to="us-gaap_MinorityInterest_637243599506496522" order="2" use="optional" weight="1" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfOperations" xlink:type="extended" xlink:title="00200 - Statement - Condensed Consolidated Statements of Operations" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss_637243599506496522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLoss_637243599506496522" order="1" use="optional" weight="1" priority="3" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss_637243599506496522" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss_637243599506496522" xlink:to="us-gaap_ProfitLoss_637243599506496522" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ProfitLoss_637243599506496522" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_637243599506506609" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_637243599506506609" xlink:to="us-gaap_OperatingIncomeLoss_637243599506506609" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_Revenues" xlink:label="us-gaap_Revenues_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingIncomeLoss_637243599506506609" xlink:to="us-gaap_Revenues_637243599506506609" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_CostsAndExpenses" xlink:label="us-gaap_CostsAndExpenses_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingIncomeLoss_637243599506506609" xlink:to="us-gaap_CostsAndExpenses_637243599506506609" order="2" use="optional" weight="-1" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_CostsAndExpensesExcludingDepreciationDepletionAndAmortizationAndGeneralAndAdministrativeExpenses" xlink:label="pzza_CostsAndExpensesExcludingDepreciationDepletionAndAmortizationAndGeneralAndAdministrativeExpenses_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CostsAndExpenses_637243599506506609" xlink:to="pzza_CostsAndExpensesExcludingDepreciationDepletionAndAmortizationAndGeneralAndAdministrativeExpenses_637243599506506609" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CostsAndExpenses_637243599506506609" xlink:to="us-gaap_GeneralAndAdministrativeExpense_637243599506506609" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:label="us-gaap_DepreciationDepletionAndAmortization_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CostsAndExpenses_637243599506506609" xlink:to="us-gaap_DepreciationDepletionAndAmortization_637243599506506609" order="3" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_637243599506506609" xlink:to="us-gaap_InterestIncomeExpenseNonoperatingNet_637243599506506609" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit_637243599506506609" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ProfitLoss_637243599506496522" xlink:to="us-gaap_IncomeTaxExpenseBenefit_637243599506506609" order="2" use="optional" weight="-1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncomeLossAttributableToNoncontrollingInterest" xlink:label="us-gaap_IncomeLossAttributableToNoncontrollingInterest_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss_637243599506496522" xlink:to="us-gaap_IncomeLossAttributableToNoncontrollingInterest_637243599506516523" order="2" use="optional" weight="-1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:label="us-gaap_PreferredStockDividendsIncomeStatementImpact_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_PreferredStockDividendsIncomeStatementImpact_637243599506516523" order="2" use="optional" weight="-1" priority="2" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfComprehensiveLoss" xlink:type="extended" xlink:title="00300 - Statement - Condensed Consolidated Statements of Comprehensive Loss" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ComprehensiveIncomeNetOfTax" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_637243599506516523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_637243599506516523" xlink:to="us-gaap_ProfitLoss_637243599506516523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_637243599506516523" xlink:to="us-gaap_OtherComprehensiveIncomeLossNetOfTax_637243599506516523" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeTax_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTax_637243599506516523" xlink:to="us-gaap_OtherComprehensiveIncomeLossBeforeTax_637243599506516523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentBeforeTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentBeforeTax_637243599506516523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossBeforeTax_637243599506516523" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentBeforeTax_637243599506516523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossDerivativesQualifyingAsHedgesBeforeTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossDerivativesQualifyingAsHedgesBeforeTax_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossBeforeTax_637243599506516523" xlink:to="us-gaap_OtherComprehensiveIncomeLossDerivativesQualifyingAsHedgesBeforeTax_637243599506526523" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossTax_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTax_637243599506516523" xlink:to="us-gaap_OtherComprehensiveIncomeLossTax_637243599506526523" order="2" use="optional" weight="-1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossTax_637243599506526523" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_637243599506526523" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossDerivativesQualifyingAsHedgesTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossDerivativesQualifyingAsHedgesTax_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossTax_637243599506526523" xlink:to="us-gaap_OtherComprehensiveIncomeLossDerivativesQualifyingAsHedgesTax_637243599506526523" order="2" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_NetIncomeLossAttributableToRedeemableNoncontrollingInterestNetOfTax" xlink:label="pzza_NetIncomeLossAttributableToRedeemableNoncontrollingInterestNetOfTax_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="pzza_NetIncomeLossAttributableToRedeemableNoncontrollingInterestNetOfTax_637243599506526523" order="2" use="optional" weight="-1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest" xlink:label="us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest_637243599506526523" order="3" use="optional" weight="-1" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfStockholdersDeficit" xlink:type="extended" xlink:title="00400 - Statement - Condensed Consolidated Statements of Stockholders' Deficit" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAdjustedBalance1" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAdjustedBalance1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_637243599506526523" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAdjustedBalance1" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_637243599506526523" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_CumulativeEffectOfNewAccountingPrincipleInPeriodOfAdoption" xlink:label="us-gaap_CumulativeEffectOfNewAccountingPrincipleInPeriodOfAdoption_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAdjustedBalance1" xlink:to="us-gaap_CumulativeEffectOfNewAccountingPrincipleInPeriodOfAdoption_637243599506536524" order="2" use="optional" weight="1" priority="2" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/StatementCondensedConsolidatedStatementsOfCashFlows" xlink:type="extended" xlink:title="00500 - Statement - Condensed Consolidated Statements of Cash Flows" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" order="1" use="optional" weight="1" priority="3" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_ProfitLoss_637243599506536524" order="1" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_637243599506536524" order="2" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:label="us-gaap_DepreciationDepletionAndAmortization_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_DepreciationDepletionAndAmortization_637243599506536524" order="3" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_DeferredIncomeTaxExpenseBenefit_637243599506536524" order="4" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_DecreaseIncreaseInPreferredStockOptionValuationOperatingActivities" xlink:label="pzza_DecreaseIncreaseInPreferredStockOptionValuationOperatingActivities_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="pzza_DecreaseIncreaseInPreferredStockOptionValuationOperatingActivities_637243599506536524" order="5" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ShareBasedCompensation" xlink:label="us-gaap_ShareBasedCompensation_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_ShareBasedCompensation_637243599506536524" order="6" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_OtherNoncashIncomeExpense" xlink:label="us-gaap_OtherNoncashIncomeExpense_637243599506536524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_OtherNoncashIncomeExpense_637243599506536524" order="7" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_637243599506546524" order="8" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInIncomeTaxesReceivable" xlink:label="us-gaap_IncreaseDecreaseInIncomeTaxesReceivable_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInIncomeTaxesReceivable_637243599506546524" order="9" use="optional" weight="-1" priority="4" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInInventories" xlink:label="us-gaap_IncreaseDecreaseInInventories_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInInventories_637243599506546524" order="10" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:label="us-gaap_IncreaseDecreaseInPrepaidExpense_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInPrepaidExpense_637243599506546524" order="11" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInOtherCurrentAssets_637243599506546524" order="12" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_637243599506546524" order="13" use="optional" weight="-1" priority="3" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInAccountsPayable" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_637243599506546524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable_637243599506546524" order="14" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInAccruedTaxesPayable" xlink:label="us-gaap_IncreaseDecreaseInAccruedTaxesPayable_637243599506556524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInAccruedTaxesPayable_637243599506556524" order="15" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_637243599506556524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_637243599506556524" order="16" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_IncreaseDecreaseInContractLiabilities" xlink:label="pzza_IncreaseDecreaseInContractLiabilities_637243599506556524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities_637243599506536524" xlink:to="pzza_IncreaseDecreaseInContractLiabilities_637243599506556524" order="17" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_637243599506566576" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_637243599506566576" order="2" use="optional" weight="1" priority="3" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_637243599506566576" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities_637243599506566576" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_637243599506566576" order="1" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsToAcquireNotesReceivable" xlink:label="us-gaap_PaymentsToAcquireNotesReceivable_637243599506566576" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities_637243599506566576" xlink:to="us-gaap_PaymentsToAcquireNotesReceivable_637243599506566576" order="2" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProceedsFromSaleAndCollectionOfNotesReceivable" xlink:label="us-gaap_ProceedsFromSaleAndCollectionOfNotesReceivable_637243599506566576" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities_637243599506566576" xlink:to="us-gaap_ProceedsFromSaleAndCollectionOfNotesReceivable_637243599506566576" order="3" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_637243599506566576" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities_637243599506566576" xlink:to="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_637243599506566576" order="4" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" order="3" use="optional" weight="1" priority="3" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:label="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_637243599506576551" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_637243599506576551" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_RepaymentsOfUnsecuredDebt" xlink:label="us-gaap_RepaymentsOfUnsecuredDebt_637243599506576551" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_RepaymentsOfUnsecuredDebt_637243599506576551" order="2" use="optional" weight="-1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProceedsFromRepaymentsOfLinesOfCredit" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_637243599506576551" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_637243599506576551" order="3" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsOfDividendsCommonStock" xlink:label="us-gaap_PaymentsOfDividendsCommonStock_637243599506576551" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_PaymentsOfDividendsCommonStock_637243599506576551" order="4" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:label="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_637243599506576551" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_637243599506576551" order="5" use="optional" weight="-1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsOfStockIssuanceCosts" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_637243599506586525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_PaymentsOfStockIssuanceCosts_637243599506586525" order="6" use="optional" weight="-1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_637243599506586525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_637243599506586525" order="7" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProceedsFromStockOptionsExercised" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_637243599506586525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_ProceedsFromStockOptionsExercised_637243599506586525" order="8" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsToMinorityShareholders" xlink:label="us-gaap_PaymentsToMinorityShareholders_637243599506586525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_PaymentsToMinorityShareholders_637243599506586525" order="9" use="optional" weight="-1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_637243599506586525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities_637243599506576551" xlink:to="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_637243599506586525" order="10" use="optional" weight="1" priority="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_637243599506596526" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_637243599506596526" order="4" use="optional" weight="1" priority="2" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/DisclosureUpdateToSignificantAccountingPoliciesNoncontrollingInterestAndJointVenturesDetails" xlink:type="extended" xlink:title="40201 - Disclosure - Update to Significant Accounting Policies - Noncontrolling Interest and Joint Ventures (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_IncomeLossFromContinuingOperationsBeforeIncomeTaxesAttributableToParent" xlink:label="IncomeLossFromContinuingOperationsBeforeIncomeTaxesAttributableToParent" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_637243599506596526" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="IncomeLossFromContinuingOperationsBeforeIncomeTaxesAttributableToParent" xlink:to="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_637243599506596526" order="1" use="optional" weight="-1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_637243599506596526" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="IncomeLossFromContinuingOperationsBeforeIncomeTaxesAttributableToParent" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_637243599506596526" order="2" use="optional" weight="1" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/DisclosureRevenueRecognitionTransactionPriceAllocatedToRemainingPerformanceObligationsDetails" xlink:type="extended" xlink:title="40502 - Disclosure - Revenue Recognition - Transaction Price Allocated to Remaining Performance Obligations (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_ContractWithCustomerLiability" xlink:label="us-gaap_ContractWithCustomerLiability_636906593502276579" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_RevenueRemainingPerformanceObligationCurrentYear" xlink:label="pzza_RevenueRemainingPerformanceObligationCurrentYear_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ContractWithCustomerLiability_636906593502276579" xlink:to="pzza_RevenueRemainingPerformanceObligationCurrentYear_637243599506606525" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_RemainingPerformanceObligationYearTwo" xlink:label="pzza_RemainingPerformanceObligationYearTwo_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ContractWithCustomerLiability_636906593502276579" xlink:to="pzza_RemainingPerformanceObligationYearTwo_637243599506606525" order="2" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_RemainingPerformanceObligationYearThree" xlink:label="pzza_RemainingPerformanceObligationYearThree_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ContractWithCustomerLiability_636906593502276579" xlink:to="pzza_RemainingPerformanceObligationYearThree_637243599506606525" order="3" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_RemainingPerformanceObligationYearFour" xlink:label="pzza_RemainingPerformanceObligationYearFour_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ContractWithCustomerLiability_636906593502276579" xlink:to="pzza_RemainingPerformanceObligationYearFour_637243599506606525" order="4" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_RemainingPerformanceObligationYearFive" xlink:label="pzza_RemainingPerformanceObligationYearFive_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ContractWithCustomerLiability_636906593502276579" xlink:to="pzza_RemainingPerformanceObligationYearFive_637243599506606525" order="5" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_RemainingPerformanceObligationAfterFifthYear" xlink:label="pzza_RemainingPerformanceObligationAfterFifthYear_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ContractWithCustomerLiability_636906593502276579" xlink:to="pzza_RemainingPerformanceObligationAfterFifthYear_637243599506606525" order="6" use="optional" weight="1" priority="2" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/DisclosureCommonStockAndSeriesBConvertiblePreferredStockCashDividendDetails" xlink:type="extended" xlink:title="40603 - Disclosure - Common Stock and Series B Convertible Preferred Stock - Cash Dividend (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PaymentsOfDividends" xlink:label="us-gaap_PaymentsOfDividends" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_PaymentsOfDividendCommonStock" xlink:label="pzza_PaymentsOfDividendCommonStock_637243599506606525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PaymentsOfDividends" xlink:to="pzza_PaymentsOfDividendCommonStock_637243599506606525" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_CommonStockDividendsPaidToPreferredShareholders" xlink:label="pzza_CommonStockDividendsPaidToPreferredShareholders_637243599506616525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PaymentsOfDividends" xlink:to="pzza_CommonStockDividendsPaidToPreferredShareholders_637243599506616525" order="2" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_DividendsPaidPreferredStock" xlink:label="pzza_DividendsPaidPreferredStock_637243599506616525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PaymentsOfDividends" xlink:to="pzza_DividendsPaidPreferredStock_637243599506616525" order="3" use="optional" weight="1" priority="2" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/DisclosureEarningsLossPerShareDetails" xlink:type="extended" xlink:title="40701 - Disclosure - Earnings (Loss) Per Share (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_635463971911717187" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_637243599506616525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_635463971911717187" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_637243599506616525" order="1" use="optional" weight="1" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:label="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_637243599506616525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_635463971911717187" xlink:to="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_637243599506616525" order="2" use="optional" weight="1" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/DisclosureOtherGeneralExpensesIncomeDetails" xlink:type="extended" xlink:title="41001 - Disclosure - Other General Expenses (Income) (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_AdministrativeExpense" xlink:label="pzza_AdministrativeExpense_637243599506616525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="pzza_AdministrativeExpense_637243599506616525" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_LossContingencyLossInPeriod" xlink:label="us-gaap_LossContingencyLossInPeriod_637243599506616525" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="us-gaap_LossContingencyLossInPeriod_637243599506616525" order="2" use="optional" weight="1" priority="3" />
    <loc xlink:type="locator" xlink:href="pzza-20200506.xsd#pzza_OtherGeneralIncomeExpenses" xlink:label="pzza_OtherGeneralIncomeExpenses_637243599506626524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="pzza_OtherGeneralIncomeExpenses_637243599506626524" order="3" use="optional" weight="-1" priority="2" />
  </calculationLink>
  <calculationLink xlink:role="http://www.papajohns.com/role/DisclosureSegmentInformationScheduleOfSegmentReportingInformationBySegmentDetails" xlink:type="extended" xlink:title="41102 - Disclosure - Segment Information - Schedule of Segment Reporting Information, by Segment (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_637243599506626524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentGross_637243599506626524" order="1" use="optional" weight="1" priority="2" />
    <loc xlink:type="locator" xlink:href="http://xbrl.fasb.org/us-gaap/2019/elts/us-gaap-2019-01-31.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_637243599506626524" />
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_637243599506626524" order="2" use="optional" weight="-1" priority="2" />
  </calculationLink>
</link:linkbase>
