Stockholders' Equity - Shares of Common Stock Outstanding (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Balance (in shares)	38,117,840	38,193,000	39,023,000
Common stock issued for employee stock plans (in shares)	663,000	839,000	712,000
Repurchase of common stock (in shares)	(700,000)	(900,000)
Balance (in shares)	38,030,252	38,117,840	38,193,000
Number of shares repurchased in settlement of employee tax withholding obligations	11,945	31,644	8,070
Value of shares repurchased in settlement of employee tax withholding obligations	$ 3.5	$ 7.2	$ 1.5
Repurchase of common stock from employees
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Repurchase of common stock (in shares)	(12,000)	(32,000)	(8,000)
Share repurchase program
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Repurchase of common stock (in shares)	(739,000)	(882,000)	(1,534,000)