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Income Taxes (Details) (USD $)
In Thousands, unless otherwise specified
 3 Months Ended 12 Months Ended
Jan. 03, 2015
Sep. 27, 2014
Jun. 28, 2014
Mar. 29, 2014
Dec. 28, 2013
Sep. 28, 2013
Jun. 29, 2013
Mar. 30, 2013
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Income (loss) before (provision) benefit for income taxes:                      
U.S.                 $ 20,899us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic $ 13,659us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic $ (27,290)us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic
Foreign                 2,416us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign 4,259us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign (30,733)us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign
Income (loss) before (provision) benefit for income taxes 6,022us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 5,575us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 6,334us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 5,384us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 5,221us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 5,952us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 3,368us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 3,377us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 23,315us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 17,918us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments (58,023)us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments
Components of income tax provision (benefit)                      
Income tax provision (benefit)                 9,908us-gaap_IncomeTaxExpenseBenefit 6,683us-gaap_IncomeTaxExpenseBenefit (5,180)us-gaap_IncomeTaxExpenseBenefit
Currently payable:                      
Federal                 8,585us-gaap_CurrentFederalTaxExpenseBenefit 1,241us-gaap_CurrentFederalTaxExpenseBenefit 3,637us-gaap_CurrentFederalTaxExpenseBenefit
Foreign                 876us-gaap_CurrentForeignTaxExpenseBenefit 1,264us-gaap_CurrentForeignTaxExpenseBenefit 50us-gaap_CurrentForeignTaxExpenseBenefit
State                 1,878us-gaap_CurrentStateAndLocalTaxExpenseBenefit 254us-gaap_CurrentStateAndLocalTaxExpenseBenefit 1,015us-gaap_CurrentStateAndLocalTaxExpenseBenefit
Currently payable                 11,339us-gaap_CurrentIncomeTaxExpenseBenefit 2,759us-gaap_CurrentIncomeTaxExpenseBenefit 4,702us-gaap_CurrentIncomeTaxExpenseBenefit
Deferred:                      
Federal                 (1,068)us-gaap_DeferredFederalIncomeTaxExpenseBenefit 3,592us-gaap_DeferredFederalIncomeTaxExpenseBenefit (8,163)us-gaap_DeferredFederalIncomeTaxExpenseBenefit
Foreign                 (505)us-gaap_DeferredForeignIncomeTaxExpenseBenefit (238)us-gaap_DeferredForeignIncomeTaxExpenseBenefit 21us-gaap_DeferredForeignIncomeTaxExpenseBenefit
State                 142us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit 570us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit (1,740)us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit
Deferred                 (1,431)us-gaap_IncreaseDecreaseInDeferredIncomeTaxes 3,924us-gaap_IncreaseDecreaseInDeferredIncomeTaxes (9,882)us-gaap_IncreaseDecreaseInDeferredIncomeTaxes
Provision (benefit) for income taxes                 $ 9,908us-gaap_IncomeTaxExpenseBenefit $ 6,683us-gaap_IncomeTaxExpenseBenefit $ (5,180)us-gaap_IncomeTaxExpenseBenefit
Reconciliation of tax rates with federal statutory rate                      
Federal statutory rate (as a percent)                 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate (35.00%)us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate
State income taxes, net of federal income tax benefit (as a percent)                 3.60%us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes 4.40%us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes (1.30%)us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes
Goodwill impairment (as a percent)                     20.60%us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses
Foreign losses benefited (as a percent)                 (1.80%)crai_EffectiveIncomeTaxRateReconciliationForeignLossesBenefited (2.80%)crai_EffectiveIncomeTaxRateReconciliationForeignLossesBenefited (0.10%)crai_EffectiveIncomeTaxRateReconciliationForeignLossesBenefited
Losses not benefited (as a percent)                 0.60%crai_EffectiveIncomeTaxRateReconciliationLossesNotBenefited 0.30%crai_EffectiveIncomeTaxRateReconciliationLossesNotBenefited 4.20%crai_EffectiveIncomeTaxRateReconciliationLossesNotBenefited
Foreign rate differential (as a percent)                 0.60%us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential (0.40%)us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential 2.10%us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential
Foreign tax credit (as a percent)                   (0.10%)us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsForeign (0.50%)us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsForeign
Uncertain tax positions (as a percent)                 0.70%us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies (2.10%)us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies  
Impact of NeuCo's tax provision charges (as a percent)                 0.90%crai_EffectiveIncomeTaxRateReconciliationTaxProvisionChargesOfSubsidiary 1.50%crai_EffectiveIncomeTaxRateReconciliationTaxProvisionChargesOfSubsidiary 0.10%crai_EffectiveIncomeTaxRateReconciliationTaxProvisionChargesOfSubsidiary
Permanently disallowed expenses (as a percent)                 2.10%us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense 1.60%us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense 1.00%us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense
Prior period adjustments (as a percent)                 3.00%us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes    
Release of valuation allowance (as a percent)                 (2.20%)us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance    
Other (as a percent)                   (0.10%)us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments  
Effective tax rate (as a percent)                 42.50%us-gaap_EffectiveIncomeTaxRateContinuingOperations 37.30%us-gaap_EffectiveIncomeTaxRateContinuingOperations (8.90%)us-gaap_EffectiveIncomeTaxRateContinuingOperations