Fair Value Measurement - Additional Information (Details) - USD ($)	3 Months Ended		6 Months Ended
	Feb. 28, 2025	Feb. 29, 2024	Feb. 28, 2025	Feb. 29, 2024	Aug. 31, 2024
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Foreign Currency Contract, Liability/Asset, Fair Value Disclosure	$ 100,000		$ 100,000		$ 300,000
Long-term Debt	192,500,000		192,500,000		195,000,000
Interest Rate Cash Flow Hedge Derivative at Fair Value, Net	100,000		100,000		100,000
Derivative Instruments in Hedges, at Fair Value, Net	1,000,000.0		1,000,000.0		(1,600,000)
Increase (Decrease) in Fair Value of Hedged Item in Interest Rate Fair Value Hedge	(100,000)	$ 100,000	100,000	$ (100,000)
Revolving Credit Facility
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term Debt	$ 0		$ 0		$ 0