Stock-based Compensation - Schedule of Market Share Units Activity (Details) - Market Share Units - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Number of Units
Beginning outstanding (in shares)	36,634
Granted (in shares)	14,233
Performance factor adjustments (in shares)	1,941
Converted to shares of common stock (in shares)	(11,631)
Forfeited (in shares)	(338)
Ending outstanding (in shares)	40,839	36,634
Weighted-Average Grant Date Fair Value Per Unit
Beginning outstanding (in dollars per share)	$ 213.13
Granted (in dollars per share)	281.09	$ 226.30	$ 184.15
Performance factor adjustments (in dollars per share)	230.88
Converted to shares of common stock (in dollars per share)	230.90
Forfeited (in dollars per share)	195.69
Ending outstanding (in dollar par share)	$ 232.74	$ 213.13
Outstanding, aggregate intrinsic value	$ 8,823
Percent of original target number of vested shares	100.00%
Maximum
Weighted-Average Grant Date Fair Value Per Unit
Percent of original target number of vested shares	200.00%