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Business and summary of significant accounting policies - Effect of Topic 606 to Statement of Operations (Details) - USD ($) $ / shares in Units, $ in Thousands | 3 Months Ended | 12 Months Ended
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Sep. 30, 2019 | Jun. 30, 2019 | Mar. 31, 2019 | Dec. 31, 2018 | Sep. 30, 2018 | Jun. 30, 2018 | Mar. 31, 2018 | Dec. 31, 2017 | Sep. 30, 2019 | Sep. 30, 2018 | Sep. 30, 2017
Revenue, Initial Application Period Cumulative Effect Transition [Line Items] |  |  |  |  |  |  |  |  |  |  |
Revenue | $ 754,966 | $ 730,710 | $ 736,520 | $ 664,619 | $ 558,446 | $ 597,855 | $ 612,787 | $ 623,148 | $ 2,886,815 | $ 2,392,236 | $ 2,450,961
Income before income taxes |  |  |  |  |  |  |  |  | 317,320 | 299,209 | 314,235
Provision for income taxes |  |  |  |  |  |  |  |  | 76,825 | 78,393 | 102,053
Net income | 60,041 | 62,965 | 61,766 | 55,723 | 45,516 | 60,242 | 55,106 | 59,952 | 240,495 | 220,816 | 212,182
(Loss)/income attributable to noncontrolling interests |  |  |  |  |  |  |  |  | (329) | 65 | 2,756
Net income attributable to MAXIMUS | $ 60,089 | $ 62,898 | $ 61,924 | $ 55,913 | $ 46,307 | $ 59,861 | $ 55,492 | $ 59,091 | $ 240,824 | $ 220,751 | $ 209,426
Basic earnings per share attributable to MAXIMUS (in dollars per share) | $ 0.93 | $ 0.98 | $ 0.96 | $ 0.86 | $ 0.71 | $ 0.91 | $ 0.84 | $ 0.90 | $ 3.73 | $ 3.37 | $ 3.19
Diluted earnings per share attributable to MAXIMUS (in dollars per share) | $ 0.93 | $ 0.97 | $ 0.96 | $ 0.86 | $ 0.71 | $ 0.91 | $ 0.84 | $ 0.89 | $ 3.72 | $ 3.35 | $ 3.17
Accounting Standards Update 2014-09 | Balance under previous accounting guidance |  |  |  |  |  |  |  |  |  |  |
Revenue, Initial Application Period Cumulative Effect Transition [Line Items] |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | $ 2,883,697 |  |
Income before income taxes |  |  |  |  |  |  |  |  | 314,202 |  |
Provision for income taxes |  |  |  |  |  |  |  |  | 75,539 |  |
Net income |  |  |  |  |  |  |  |  | 238,663 |  |
(Loss)/income attributable to noncontrolling interests |  |  |  |  |  |  |  |  | (977) |  |
Net income attributable to MAXIMUS |  |  |  |  |  |  |  |  | $ 239,640 |  |
Basic earnings per share attributable to MAXIMUS (in dollars per share) |  |  |  |  |  |  |  |  | $ 3.72 |  |
Diluted earnings per share attributable to MAXIMUS (in dollars per share) |  |  |  |  |  |  |  |  | $ 3.70 |  |
Accounting Standards Update 2014-09 | Adjustments due to adoption of new standard |  |  |  |  |  |  |  |  |  |  |
Revenue, Initial Application Period Cumulative Effect Transition [Line Items] |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | $ 3,118 |  |
Income before income taxes |  |  |  |  |  |  |  |  | 3,118 |  |
Provision for income taxes |  |  |  |  |  |  |  |  | 1,286 |  |
Net income |  |  |  |  |  |  |  |  | 1,832 |  |
(Loss)/income attributable to noncontrolling interests |  |  |  |  |  |  |  |  | 648 |  |
Net income attributable to MAXIMUS |  |  |  |  |  |  |  |  | $ 1,184 |  |
Basic earnings per share attributable to MAXIMUS (in dollars per share) |  |  |  |  |  |  |  |  | $ 0.01 |  |
Diluted earnings per share attributable to MAXIMUS (in dollars per share) |  |  |  |  |  |  |  |  | $ 0.02 |  |

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