Stockholders' Equity - Shares of Common Stock Outstanding (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2021	Feb. 29, 2020	Feb. 28, 2021	Feb. 29, 2020
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning Balance (in shares)			38,030,252	38,118,000
Common stock issued for employee stock plans (in shares)			176,000	348,000
Repurchase of common stock (in shares)	(221,959)	(267,500)	(353,759)	(610,500)
Ending Balance (in shares)	37,844,998	37,849,000	37,844,998	37,849,000
Number of shares repurchased in settlement of employee tax withholding obligations (in shares)			7,447	6,252
Value of shares repurchased in settlement of employee tax withholding obligations			$ 2.4	$ 1.6
Repurchase of common stock from employees
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Repurchase of common stock (in shares)			(7,000)	(6,000)
Share repurchase program
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Repurchase of common stock (in shares)			(354,000)	(611,000)