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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 4,631,018 | $ 4,254,485 | $ 3,461,537
United States |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 3,867,354 | $ 3,555,394 | $ 2,962,611
United States | Revenue Benchmark | Geographic Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 83.50% | 83.60% | 85.60%
United Kingdom |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 410,587 | $ 286,432 | $ 246,334
United Kingdom | Revenue Benchmark | Geographic Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 8.90% | 6.70% | 7.10%
Australia |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 173,078 | $ 244,995 | $ 147,156
Australia | Revenue Benchmark | Geographic Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 3.70% | 5.80% | 4.30%
Rest of world |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 179,999 | $ 167,664 | $ 105,436
Rest of world | Revenue Benchmark | Geographic Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 3.90% | 3.90% | 3.00%
U. S. federal government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,189,303 | $ 1,805,131 | $ 1,559,165
U. S. federal government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 47.30% | 42.40% | 45.10%
U.S. state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,605,457 | $ 1,654,555 | $ 1,344,227
U.S. state government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 34.70% | 38.90% | 38.80%
International government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 722,192 | $ 663,180 | $ 467,185
International government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 15.60% | 15.60% | 13.50%
Other, including local municipalities and commercial customers |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 114,066 | $ 131,619 | $ 90,960
Other, including local municipalities and commercial customers | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 2.40% | 3.10% | 2.60%
Performance-based |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,091,608 | $ 1,416,562 | $ 1,109,153
Performance-based | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 45.20% | 33.30% | 32.10%
Cost-plus |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,248,759 | $ 1,237,995 | $ 1,578,912
Cost-plus | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 27.00% | 29.10% | 45.60%
Fixed price |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 627,402 | $ 553,645 | $ 471,505
Fixed price | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 13.50% | 13.00% | 13.60%
Time and materials |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 663,249 | $ 1,046,283 | $ 301,967
Time and materials | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 14.30% | 24.60% | 8.70%
Program Operations |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,596,801 | $ 2,755,820 | $ 2,395,618
Program Operations | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 56.10% | 64.80% | 69.20%
Clinical Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,176,081 | $ 699,424 | $ 539,018
Clinical Services | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 25.40% | 16.40% | 15.60%
Employment & Other |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 551,755 | $ 463,695 | $ 318,431
Employment & Other | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 11.90% | 10.90% | 9.20%
Technology Solutions |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 306,381 | $ 335,546 | $ 208,470
Technology Solutions | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 6.60% | 7.90% | 6.00%

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