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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Sep. 30, 2021 | Sep. 30, 2020 | Sep. 30, 2019
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 4,254,485 | $ 3,461,537 | $ 2,886,815
United States |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 3,555,394 | 2,962,611 | 2,287,685
United Kingdom |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 286,432 | 246,334 | 293,695
Australia |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 244,995 | 147,156 | 198,795
Rest of world |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 167,664 | 105,436 | 106,640
Total U.S. state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,654,555 | 1,344,227 | 1,166,937
New York State government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 371,917 | 355,282 | 362,724
Other U.S. state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,282,638 | 988,945 | 804,213
United States Federal Government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,805,131 | 1,559,165 | 1,040,980
International government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 663,180 | 467,185 | 558,599
Other, including local municipalities and commercial customers |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 131,619 | 90,960 | 120,299
Performance-based |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,416,562 | 1,109,153 | 1,193,075
Cost-plus |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,237,995 | 1,578,912 | 1,088,541
Fixed price |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 553,645 | 471,505 | 441,146
Time and materials |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,046,283 | 301,967 | 164,053
U.S. Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,662,110 | 1,329,274 | 1,176,488
U.S. Federal Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,893,284 | 1,633,337 | 1,111,197
Outside the U.S. |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 699,091 | 498,926 | 599,130
Workforce services | Outside the U.S. |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 358,088 | 206,657 | 272,801
Program administration | U.S. Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,154,939 | 945,125 | 883,772
Program administration | U.S. Federal Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 1,273,850 | 1,288,741 | 779,573
Program administration | Outside the U.S. |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 107,643 | 66,002 | 63,734
Technology solutions | U.S. Federal Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 278,232 | 169,259 | 160,342
Assessments and appeals | U.S. Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 138,297 | 141,446 | 136,109
Assessments and appeals | U.S. Federal Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 341,202 | 175,337 | 171,282
Assessments and appeals | Outside the U.S. |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 225,314 | 218,704 | 252,447
Employment and children services | U.S. Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 320,653 | 191,061 | 100,454
Other | U.S. Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | 48,221 | 51,642 | 56,153
Other | Outside the U.S. |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 8,046 | $ 7,563 | $ 10,148

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