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Stock-Based Compensation - Schedule of Equity-Based Compensation Plans (Details) - $ / shares	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Equity-based compensation plans
Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Performance Share Awards (in shares)	1,115,679
Weighted-Average Exercise Price of Outstanding Options (in dollars per share)	$ 77.96	$ 74.38	$ 62.62	$ 57.03
Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (in shares)	3,310,992
Equity compensation plans approved by security holders [Member]
Equity-based compensation plans
Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Performance Share Awards (in shares)	1,115,679
Weighted-Average Exercise Price of Outstanding Options (in dollars per share)	$ 77.96
Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (in shares)	3,310,992
Equity Compensation Plans Not Approved By Security Holders [Member]
Equity-based compensation plans
Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Performance Share Awards (in shares)	0
Weighted-Average Exercise Price of Outstanding Options (in dollars per share)	$ 0
Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (in shares)	0

X

- Definition

Represents the number of shares (or other type of equity) to be issued under the equity-based compensation plan.

+ References

No definition available.

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- Definition

Represents the remaining number of shares (or other type of equity) available for future issuance under the equity-based compensation plan.

+ References

No definition available.

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- Definition

Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

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