Share-based Compensation - Assumptions Used to Estimate Fair Value Using Monte Carlo Model (Details) - Performance-based Shares - $ / shares	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected term (in years)	1 year 11 months 4 days	2 years 1 month 24 days	2 years 18 days
Risk-free rate of return (in percent)	4.80%	4.40%	0.50%
Expected volatility (in percent)	21.70%	28.90%	28.30%
Expected dividend yield (in percent)	0.80%	0.80%	0.80%
Fair value per performance-based share granted (in dollars per share)	$ 281.85	$ 221.32	$ 186.50