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Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) - USD ($)
 3 Months Ended 6 Months Ended
Mar. 31, 2023
Mar. 31, 2023
Sep. 30, 2022
Goodwill [Line Items]      
Goodwill     $ 18,109,000,000
Accumulated impairment loss     (781,000,000)
Goodwill [Roll Forward]      
Balance at beginning of period   $ 17,328,000,000  
Acquisitions   69,000,000  
Impairments $ (184,000,000) (184,000,000)  
Foreign currency translation and other   346,000,000  
Balance at end of period 17,559,000,000 17,559,000,000  
Silent-Aire      
Goodwill [Roll Forward]      
Balance at end of period 0 0  
Building Solutions North America      
Goodwill [Line Items]      
Goodwill     9,630,000,000
Accumulated impairment loss     (659,000,000)
Goodwill [Roll Forward]      
Balance at beginning of period   8,971,000,000  
Acquisitions   0  
Impairments   0  
Foreign currency translation and other   8,000,000  
Balance at end of period 8,979,000,000 8,979,000,000  
Building Solutions EMEA/LA      
Goodwill [Line Items]      
Goodwill     1,772,000,000
Accumulated impairment loss     (47,000,000)
Goodwill [Roll Forward]      
Balance at beginning of period   1,725,000,000  
Acquisitions   16,000,000  
Impairments   0  
Foreign currency translation and other   183,000,000  
Balance at end of period 1,924,000,000 1,924,000,000  
Building Solutions Asia Pacific      
Goodwill [Line Items]      
Goodwill     1,116,000,000
Accumulated impairment loss     0
Goodwill [Roll Forward]      
Balance at beginning of period   1,116,000,000  
Acquisitions   0  
Impairments   0  
Foreign currency translation and other   53,000,000  
Balance at end of period 1,169,000,000 1,169,000,000  
Global Products      
Goodwill [Line Items]      
Goodwill     5,591,000,000
Accumulated impairment loss     $ (75,000,000)
Goodwill [Roll Forward]      
Balance at beginning of period   5,516,000,000  
Acquisitions   53,000,000  
Impairments   (184,000,000)  
Foreign currency translation and other   102,000,000  
Balance at end of period $ 5,487,000,000 $ 5,487,000,000