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Receivables - Rollforward of Combined Allowances for Doubtful Accounts Related to Trade and Other Accounts Receivable (Detail) - USD ($) $ in Millions | 12 Months Ended
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Jan. 01, 2022 | Jan. 02, 2021
Allowances for credit losses: |  |
Beginning of period | $ 26.3 | $ 20.9
Provision for credit losses | 15.5 | 18.9
Charge-offs | (13.6) | (13.6)
Recoveries | 0.0 | 0.2
Currency translation | (0.9) | (0.1)
End of period | $ 27.3 | $ 26.3

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- Definition Accounts Receivable, Allowance For Credit Loss, Foreign Currency Translation Increase (Decrease) + References No definition available. + Details
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Namespace Prefix: | sna_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Amount of allowance for credit loss on accounts receivable, classified as current. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 210 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(4) -URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 310 -SubTopic 10 -Section 50 -Paragraph 4 -URI http://asc.fasb.org/extlink&oid=123577603&loc=d3e5074-111524 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 326 -SubTopic 20 -Section 45 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=124255206&loc=SL82895884-210446 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Amount of increase in allowance for credit loss on accounts receivable, from recovery. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 326 -SubTopic 20 -Section 50 -Paragraph 13 -Subparagraph (e) -URI http://asc.fasb.org/extlink&oid=124255953&loc=SL82919249-210447 + Details
Name: | us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period. + References No definition available. + Details
Name: | us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Amount of direct write-downs of accounts receivable charged against the allowance. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 326 -SubTopic 20 -Section 50 -Paragraph 13 -Subparagraph (d) -URI http://asc.fasb.org/extlink&oid=124255953&loc=SL82919249-210447 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Amount of expense (reversal of expense) for expected credit loss on accounts receivable. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 326 -SubTopic 20 -Section 50 -Paragraph 13 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=124255953&loc=SL82919249-210447 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 220 -SubTopic 10 -Section S99 -Paragraph 2 -Subparagraph (SX 210.5-03(5)) -URI http://asc.fasb.org/extlink&oid=123367319&loc=SL114868664-224227 + Details
Name: | us-gaap_ProvisionForDoubtfulAccounts
Namespace Prefix: | us-gaap_
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Balance Type: | debit
Period Type: | duration