Stock-based Compensation - Activity of Restricted Stock Units (Details)	12 Months Ended
	Sep. 30, 2025 $ / shares shares
Performance-contingent Restricted Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Nonvested, units (in shares) | shares	289,205
Granted, units (in shares) | shares	103,780
Adjusted for performance, units (in shares) | shares	21,469
Vested, units (in shares) | shares	(100,784)
Forfeited, units (in shares) | shares	(69,166)
Nonvested, units (in shares) | shares	244,504
Nonvested, weighted average grant date fair value (in dollars per share) | $ / shares	$ 73.36
Granted, weighted average grant date fair value (in dollars per share) | $ / shares	76.52
Adjusted for performance, weighted average grant date fair value (in dollars per share) | $ / shares	65.02
Vested, weighted average grant date fair value (in dollars per share) | $ / shares	65.02
Forfeited, weighted average grant date fair value (in dollars per share) | $ / shares	74.67
Nonvested, weighted average grant date fair value (in dollars per share) | $ / shares	$ 75.62
Time-vested Restricted Stock
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Nonvested, units (in shares) | shares	85,559
Granted, units (in shares) | shares	57,030
Vested, units (in shares) | shares	(42,677)
Forfeited, units (in shares) | shares	(23,348)
Nonvested, units (in shares) | shares	76,564
Nonvested, weighted average grant date fair value (in dollars per share) | $ / shares	$ 64.13
Granted, weighted average grant date fair value (in dollars per share) | $ / shares	72
Vested, weighted average grant date fair value (in dollars per share) | $ / shares	66.36
Forfeited, weighted average grant date fair value (in dollars per share) | $ / shares	67.61
Nonvested, weighted average grant date fair value (in dollars per share) | $ / shares	$ 67.2