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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Pre-tax share-based compensation expense $ 85.0 $ 100.0 $ 88.0  
Income tax benefit related to share-based compensation expense 13.0 $ 16.0 $ 15.0  
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures $ 76.0      
Weighted average period for recognition of total unrecognized compensation cost 1 year 7 months 6 days      
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Expiration period 10 years      
Vesting period 3 years      
Per share weighted average fair value of stock options granted (in dollars per share) $ 93.48 $ 85.63 $ 77.62  
Total intrinsic value of stock options exercised $ 75.0 $ 27.0 $ 70.0  
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 3 years 3 years    
Percent payout 0.00% 92.00% 177.00%  
Payout percentage in December 2020 for performance period ending September 30, 2020 70.00%      
Maximum potential shares to be delivered in payment under performance share awards (in shares) 35,000      
Weighted average grant date fair value of awards granted (in dollars per share) $ 387.72 $ 295.06 $ 340.77  
Total fair value of shares vested $ 0.0 $ 9.0 $ 13.0  
Shares granted in the period (in shares) 58,000      
Performance shares | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Percent payout     0.00% 0.00%
Performance shares | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Percent payout     200.00% 200.00%
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Weighted average grant date fair value of awards granted (in dollars per share) $ 299.05 $ 276.34 $ 263.67  
Total fair value of shares vested $ 64.0 $ 60.0 $ 54.0  
Shares granted in the period (in shares) 102,000      
Restricted stock and restricted stock units | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 1 year      
Restricted stock and restricted stock units | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 3 years      
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Weighted average grant date fair value of awards granted (in dollars per share) $ 297.10 $ 278.35 $ 261.56  
Shares granted in the period (in shares) 6,100      
2020 Long Term Incentive Plan        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Shares authorized (up to) (in shares)     13,000,000.0  
Shares available for grant (in shares) 6,200,000