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Share-based Payments (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 6 Months Ended
Mar. 31, 2022
Mar. 31, 2021
Mar. 31, 2022
Mar. 31, 2021
Sep. 30, 2021
Stock options, Weighted average exercise price          
Vesting period     3 years    
Recognized compensation expense $ 21.7 $ 24.6      
Unrecognized compensation expense $ 65.7   $ 65.7   $ 45.6
Performance Earnings Program          
Stock options, Weighted average exercise price          
Vesting period     3 years    
Weighted average grant-date fair value of stock options granted (in dollars per share) $ 85.48 $ 52.52      
Restricted Stock Units (RSUs)          
Stock options, Weighted average exercise price          
Weighted average grant-date fair value of stock options granted (in dollars per share) $ 74.32 $ 48.78      
Employee Stock Option          
Shares of stock under options          
Balance at the beginning of the period (in shares)     0.3 0.4  
Options granted (in shares)     0.0 0.0  
Options exercised (in shares)     0.0 (0.1)  
Options forfeited or expired ( in shares)     0.0 0.0  
Balance at the end of the period (in shares) 0.3 0.3 0.3 0.3  
Vested and expected to vest in the future at the end of the period (in shares) 0.2 0.2 0.2 0.2  
Stock options, Weighted average exercise price          
Balance at the beginning of the period (in dollars per share)     $ 38.72 $ 36.41  
Options granted (in dollars per share)     0 0  
Options exercised (in dollars per share)     0 31.62  
Options forfeited or expired (in dollars per share)     0 0  
Balance at the end of the period (in dollars per share) $ 38.72 $ 38.72 38.72 38.72  
Vested and expected to vest in the future at the end of the period (in dollars per share) $ 38.72 $ 38.72 $ 38.72 $ 38.72