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Leases (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Jan. 02, 2021 | Dec. 28, 2019 | Dec. 29, 2018
Lease expenses included in income statement |  |  |
Operating lease cost | $ 17,803 | $ 15,731 |
Short-term lease cost | 908 | 511 |
Variable lease cost | 6,155 | 4,461 |
Total lease cost | $ 24,866 | $ 20,703 |
Base rent expense |  |  | $ 13,200
Weighted average remaining lease term - operating leases (in years) | 8 years 7 months 6 days | 9 years 7 months 6 days |
Weighted average discount rate - operating leases | 3.60% | 3.70% |

X
- Definition This element represents the annual base payments that the lessee is obligated to make in connection with a property under the terms of an agreement classified as an operating lease. + References No definition available. + Details
Name: | crai_OperatingLeaseAnnualBaseRent
Namespace Prefix: | crai_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- References No definition available. + Details
Name: | us-gaap_IncomeAndExpensesLesseeAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Amount of lease cost recognized by lessee for lease contract. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 50 -Paragraph 4 -URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918686-209980 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 55 -Paragraph 53 -URI http://asc.fasb.org/extlink&oid=77888399&loc=SL77918982-209971 + Details
Name: | us-gaap_LeaseCost
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Amount of single lease cost, calculated by allocation of remaining cost of lease over remaining lease term. Includes, but is not limited to, single lease cost, after impairment of right-of-use asset, calculated by amortization of remaining right-of-use asset and accretion of lease liability. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 55 -Paragraph 53 -URI http://asc.fasb.org/extlink&oid=77888399&loc=SL77918982-209971 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 50 -Paragraph 4 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918686-209980 + Details
Name: | us-gaap_OperatingLeaseCost
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Weighted average discount rate for operating lease calculated at point in time. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 50 -Paragraph 4 -Subparagraph (g)(4) -URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918686-209980 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 55 -Paragraph 53 -URI http://asc.fasb.org/extlink&oid=77888399&loc=SL77918982-209971 + Details
Name: | us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent
Namespace Prefix: | us-gaap_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

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- Definition Weighted average remaining lease term for operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 55 -Paragraph 53 -URI http://asc.fasb.org/extlink&oid=77888399&loc=SL77918982-209971 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 50 -Paragraph 4 -Subparagraph (g)(3) -URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918686-209980 + Details
Name: | us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1
Namespace Prefix: | us-gaap_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | instant

X
- Definition Amount of short-term lease cost, excluding expense for lease with term of one month or less. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 50 -Paragraph 4 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918686-209980 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 55 -Paragraph 53 -URI http://asc.fasb.org/extlink&oid=77888399&loc=SL77918982-209971 + Details
Name: | us-gaap_ShortTermLeaseCost
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Amount of variable lease cost, excluded from lease liability, recognized when obligation for payment is incurred for finance and operating leases. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 50 -Paragraph 4 -Subparagraph (d) -URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918686-209980 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 55 -Paragraph 53 -URI http://asc.fasb.org/extlink&oid=77888399&loc=SL77918982-209971 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration