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Acquisitions and Divestitures - Narrative (Details) $ in Millions			1 Months Ended	3 Months Ended	12 Months Ended
	Jan. 01, 2025 USD ($)	May 15, 2023 USD ($)	Nov. 30, 2022 USD ($)	Aug. 31, 2025 USD ($)	Aug. 31, 2025 USD ($)	Aug. 31, 2024 USD ($) acquisition	Aug. 31, 2023 USD ($)	Jun. 01, 2025 USD ($)
Business Combination [Line Items]
Number of acquisitions | acquisition						0
Adjustments to provisional amounts from acquired businesses					$ 31.1
Goodwill				$ 1,495.5	1,495.5	$ 1,098.7	$ 1,097.9	$ 1,500.0
Weighted Average Useful Life (Years)	13 years
Loss on sale of business					0.0	0.0	11.2
Disposal Group, Not Discontinued Operations | Sunoptics Business
Business Combination [Line Items]
Assets held for sale, total			$ 15.1
Loss on sale of business			$ 11.2
AIS
Business Combination [Line Items]
Goodwill				479.5	479.5	$ 83.6	$ 83.5
QSC, LLC
Business Combination [Line Items]
Cash consideration	$ 1,240.7
Acquisition related professional fees expensed					$ 23.8
Business combination goodwill expected tax deductible amount	350.0
Finite-lived intangible assets acquired, cumulative catch-up amortization expense				$ 6.9
Goodwill	394.6
Identifiable intangible assets	$ 713.9
KE2 Therm Solutions, Inc.
Business Combination [Line Items]
Identifiable intangible assets		$ 18.0
Weighted Average Useful Life (Years)		15 years
KE2 Therm Solutions, Inc. | AIS
Business Combination [Line Items]
Goodwill		$ 15.0

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