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Stock-based Compensation (Narrative) (Details) - USD ($) | 12 Months Ended
--- | ---
Aug. 31, 2023 | Aug. 31, 2022 | Aug. 31, 2021
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Number of shares authorized under stock plan | 1,000,000 |  |
Number of shares available for grant | 172,878 |  |
Employee service share-based, Tax benefit from compensation expense | $ 1,300,000 | $ 1,500,000 | $ 2,000,000
Restricted Stock Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Granted (in shares) | 23,732 |  |
Employee service share-based, Tax benefit from compensation expense | $ 800,000 | $ 600,000 | $ 1,900,000
Compensation cost not yet recognized | $ 1,000,000 |  |
Remaining weighted-average vesting periods | 1 year 9 months 18 days |  |
Weighted-average grant date fair value (in dollars per share) | $ 167.05 | $ 217.03 | $ 208.29
Intrinsic value of shares converted | $ 3,700,000 | $ 3,000,000 | $ 8,500,000
Market Share Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Granted (in shares) | 13,695 |  |
Employee service share-based, Tax benefit from compensation expense |  | $ 900,000 | $ 1,300,000
Compensation cost not yet recognized | $ 2,400,000 |  |
Remaining weighted-average vesting periods | 1 year 10 months 17 days |  |
Weighted-average grant date fair value (in dollars per share) | $ 184.15 | $ 232.99 | $ 184.96
Intrinsic value of shares converted | $ 0 | $ 4,400,000 | $ 5,900,000
Expected volatility period | 2 years 10 months 20 days | 2 years 10 months 20 days | 2 years 10 months 17 days
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] |  |  |
Period of separation from service |  |  | 6 months
Granted (in shares) | 21,990 |  |
Employee service share-based, Tax benefit from compensation expense |  | $ 800,000 | $ 0
Compensation cost not yet recognized | $ 0 |  |
Weighted-average grant date fair value (in dollars per share) | $ 170.16 | $ 227.24 | $ 197.51
Intrinsic value of shares converted | $ 0 | $ 4,000,000 |
Vesting percentage |  |  | 100.00%
Key Executives | Restricted Stock Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Vesting period | 3 years |  |
Period of separation from service | 6 months |  |
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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