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Stock-based Compensation - Narrative (Details) - USD ($) | 12 Months Ended |  |
--- | --- | --- | ---
Aug. 31, 2024 | Aug. 31, 2023 | Aug. 31, 2022 | Aug. 31, 2021 | Dec. 12, 2023 | Dec. 11, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Number of shares authorized under stock plan |  |  |  |  | 2,000,000 | 1,000,000
Number of shares available for grant | 1,106,326 |  |  |  |  |
Share-based arrangement, tax benefit | $ 1,400,000 | $ 1,300,000 | $ 1,500,000 |  |  |
Restricted Stock Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) | 19,201 |  |  |  |  |
Share-based arrangement, tax benefit | $ 1,300,000 | $ 800,000 | $ 600,000 |  |  |
Compensation cost not yet recognized | $ 1,300,000 |  |  |  |  |
Remaining weighted-average vesting periods | 1 year 8 months 19 days |  |  |  |  |
Weighted-average grant date fair value (in dollars per share) | $ 206.85 | $ 167.05 | $ 217.03 |  |  |
Intrinsic value of shares converted | $ 6,700,000 | $ 3,700,000 | $ 3,000,000.0 |  |  |
Outstanding, aggregate intrinsic value | $ 18,438,000 |  |  |  |  |
Market Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) | 14,263 |  |  |  |  |
Share-based arrangement, tax benefit |  |  | $ 900,000 |  |  |
Compensation cost not yet recognized | $ 3,300,000 |  |  |  |  |
Remaining weighted-average vesting periods | 1 year 10 months 9 days |  |  |  |  |
Weighted-average grant date fair value (in dollars per share) | $ 226.30 | $ 184.15 | $ 232.99 |  |  |
Intrinsic value of shares converted | $ 0 | $ 0 | $ 4,400,000 |  |  |
Expected volatility period | 2 years 10 months 24 days | 2 years 10 months 20 days | 2 years 10 months 20 days |  |  |
Expected dividend yield | 0.00% | 0.00% | 0.00% |  |  |
Outstanding, aggregate intrinsic value | $ 9,629,000 |  |  |  |  |
Deferred Performance Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) |  |  |  | 0 |  |
Compensation cost not yet recognized | $ 0 |  |  |  |  |
Performance Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) | 20,039 |  |  |  |  |
Period of separation from service |  |  |  | 6 months |  |
Share-based arrangement, tax benefit |  |  | $ 800,000 |  |  |
Compensation cost not yet recognized | $ 0 |  |  |  |  |
Weighted-average grant date fair value (in dollars per share) | $ 198.94 | $ 170.16 | $ 227.24 |  |  |
Intrinsic value of shares converted | $ 0 | $ 0 | $ 0 |  |  |
Outstanding, aggregate intrinsic value | $ 5,167,000 |  | $ 4,000,000.0 |  |  |
Nonemployee directors | Restricted Stock Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting period | 1 year |  |  |  |  |
High Level Employees | Restricted Stock Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting period | 3 years |  |  |  |  |
High Level Employees | Market Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting period | 3 years |  |  |  |  |
Minimum | Market Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting percentage | 0.00% |  |  |  |  |
Minimum | Performance Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting percentage | 0.00% |  |  |  |  |
Maximum | Market Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting percentage | 200.00% |  |  |  |  |
Maximum | Performance Share Units |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Vesting percentage | 100.00% |  |  |  |  |

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