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Acquisitions and Divestitures - Additional Information (Detail) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2021
Jun. 30, 2022
Jun. 30, 2021
Acquisitions And Divestitures [Line Items]      
Cash paid for business acquisition   $ 236 $ 707
Goodwill, Acquired During Period   207  
Business divestitures, net of cash divested   16 19
Goodwill, Written off Related to Sale of Business Unit   127  
Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   45  
Goodwill, Written off Related to Sale of Business Unit   29  
Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   77  
Goodwill, Written off Related to Sale of Business Unit   98  
Building Solutions North America      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   24  
Goodwill, Written off Related to Sale of Business Unit   0  
Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   61  
Goodwill, Written off Related to Sale of Business Unit   0  
Business Divestitures, Not Specific | Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Proceeds from Divestiture of Businesses $ 27   27
Business divestitures, net of cash divested     19
Goodwill, Written off Related to Sale of Business Unit     7
Business Divestitures, Not Specific | Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Proceeds from Divestiture of Businesses   18  
Business divestitures, net of cash divested   16  
Goodwill, Written off Related to Sale of Business Unit   5  
Individually Immaterial Acquisitions      
Acquisitions And Divestitures [Line Items]      
Purchase price, net of cash acquired   287 58
Cash paid for business acquisition   236 46
Individually Immaterial Acquisitions | Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   45  
Individually Immaterial Acquisitions | Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   68 21
Individually Immaterial Acquisitions | Building Solutions North America      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   24 17
Individually Immaterial Acquisitions | Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   45  
Silent-Aire      
Acquisitions And Divestitures [Line Items]      
Purchase price, net of cash acquired 755    
Cash paid for business acquisition 661    
Business Combination, Contingent Consideration, Liability 86   86
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High 250   250
Business Combination, working capital adjustment 8   $ 8
Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability   $ 43  
Silent-Aire | Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period $ 244