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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 4,904,728 | $ 4,631,018 | $ 4,254,485
U. S. federal government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,344,863 | $ 2,189,303 | $ 1,805,131
U. S. federal government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 47.80% | 47.30% | 42.40%
U.S. state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,800,814 | $ 1,605,457 | $ 1,654,555
U.S. state government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 36.70% | 34.70% | 38.90%
International government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 663,044 | $ 722,192 | $ 663,180
International government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 13.50% | 15.60% | 15.60%
Other, including local municipalities and commercial customers |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 96,007 | $ 114,066 | $ 131,619
Other, including local municipalities and commercial customers | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 2.00% | 2.50% | 3.10%
Performance-based |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,425,597 | $ 2,091,608 | $ 1,416,562
Performance-based | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 49.50% | 45.20% | 33.30%
Cost-plus |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,238,574 | $ 1,248,759 | $ 1,237,995
Cost-plus | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 25.30% | 27.00% | 29.10%
Fixed price |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 717,167 | $ 627,402 | $ 553,645
Fixed price | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 14.60% | 13.50% | 13.00%
Time and materials |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 523,390 | $ 663,249 | $ 1,046,283
Time and materials | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 10.70% | 14.30% | 24.60%
Program Operations |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,607,263 | $ 2,596,801 | $ 2,755,820
Program Operations | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 53.20% | 56.10% | 64.80%
Clinical Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,486,040 | $ 1,176,081 | $ 699,424
Clinical Services | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 30.30% | 25.40% | 16.40%
Employment & Other |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 520,981 | $ 551,755 | $ 463,695
Employment & Other | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 10.60% | 11.90% | 10.90%
Technology Solutions |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 290,444 | $ 306,381 | $ 335,546
Technology Solutions | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 5.90% | 6.60% | 7.90%

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