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Related-Party Transactions (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Shareholders |  |  |
Related-Party Transactions |  |  |
Payments for consulting services | $ 8.0 | $ 9.8 | $ 9.3

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
Name: | us-gaap_RelatedPartyTransactionLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Purchases during the period (excluding transactions that are eliminated in consolidated or combined financial statements) with related party. + References No definition available. + Details
Name: | us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Details
Name: | us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=crai_ShareholdersMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |