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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%