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Acquisitions and Divestitures (Details) $ in Millions		1 Months Ended	9 Months Ended		12 Months Ended
	May 15, 2023 USD ($)	Nov. 30, 2022 USD ($)	May 31, 2023 USD ($)	May 31, 2022 USD ($)	Aug. 31, 2022 USD ($) acquisition	Oct. 30, 2022 USD ($)	Aug. 31, 2021 USD ($)
Business Combination and Asset Acquisition [Abstract]
Number of acquisitions completed | acquisition					0
Cash outflow				$ (12.2)
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill			$ 1,096.7	1,090.9	$ 1,084.3		$ 1,094.7
Preliminary goodwill			15.2
Pre-tax loss on the sale			11.2	0.0
ISG
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill			83.4	$ 72.4	$ 70.1		$ 72.5
Preliminary goodwill			$ 15.2
KE2 Therm Solutions, Inc
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill	$ 15.2
Identified intangible assets	$ 18.0
Weighted average amortization period in years	15 years
Sunoptics Prismatic Skylights Business | Disposal Group, Not Discontinued Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Assets transferred						$ 15.1
Pre-tax loss on the sale		$ 11.2

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