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Supplemental Disaggregated Information (Details) $ in Millions	12 Months Ended
	Aug. 31, 2020 USD ($) Segment	Aug. 31, 2019 USD ($)	Aug. 31, 2018 USD ($)
Geographic Distribution
Number of reportable segments | Segment	1
Net sales	$ 3,326.3	$ 3,672.7	$ 3,680.1
Operating profit:	353.9	462.9	460.8
Income before provision for income taxes:	324.7	424.9	425.9
Long-lived assets	366.1	297.3	308.4
Domestic
Geographic Distribution
Net sales	2,925.0	3,277.4	3,292.6
Operating profit:	300.6	419.3	419.0
Income before provision for income taxes:	274.2	386.4	386.4
Long-lived assets	301.2	248.9	256.4
International
Geographic Distribution
Net sales	401.3	395.3	387.5
Operating profit:	53.3	43.6	41.8
Income before provision for income taxes:	50.5	38.5	39.5
Long-lived assets	$ 64.9	$ 48.4	$ 52.0
Sales of lighting solutions, excluding services | Revenue source
Geographic Distribution
Sales as percentage of total sales (percent)	5.00%	5.00%	5.00%
Lighting and Building Management Solutions | Sales of lighting solutions, excluding services | Revenue source
Geographic Distribution
Sales as percentage of total sales (percent)	99.00%	99.00%	99.00%

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