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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($)
$ in Millions
 9 Months Ended
May 31, 2023
May 31, 2022
Goodwill [Roll Forward]    
Goodwill, beginning balance $ 1,084.3 $ 1,094.7
Provisional amounts from acquired businesses 15.2  
Derecognitions for divestitures (0.7)  
Adjustments to provisional amounts from acquired businesses   0.6
Foreign currency translation adjustments (2.1) (4.4)
Goodwill, ending balance 1,096.7 1,090.9
ABL    
Goodwill [Roll Forward]    
Goodwill, beginning balance 1,014.2 1,022.2
Derecognitions for divestitures (0.7)  
Adjustments to provisional amounts from acquired businesses   0.6
Foreign currency translation adjustments (0.2) (4.3)
Goodwill, ending balance 1,013.3 1,018.5
ISG    
Goodwill [Roll Forward]    
Goodwill, beginning balance 70.1 72.5
Provisional amounts from acquired businesses 15.2  
Derecognitions for divestitures 0.0  
Adjustments to provisional amounts from acquired businesses   0.0
Foreign currency translation adjustments (1.9) (0.1)
Goodwill, ending balance 83.4 $ 72.4
Acuity Brands Lighting, Inc.    
Goodwill [Roll Forward]    
Provisional amounts from acquired businesses $ 0.0