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Exit and Disposal Activities - Restructuring Accrual Rollforward (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2022
Jan. 02, 2021
Restructuring Reserve [Roll Forward]    
Restructuring reserve, beginning balance $ 10.0 $ 0.0
Provision 0.0 12.2
Usage (3.0) (2.2)
Restructuring reserve, ending balance 7.0 10.0
Commercial & Industrial Group    
Restructuring Reserve [Roll Forward]    
Restructuring reserve, beginning balance 5.8 0.0
Provision 0.0 6.4
Usage (1.5) (0.6)
Restructuring reserve, ending balance 4.3 5.8
Snap-on Tools Group    
Restructuring Reserve [Roll Forward]    
Restructuring reserve, beginning balance 0.4 0.0
Provision 0.0 0.6
Usage (0.1) (0.2)
Restructuring reserve, ending balance 0.3 0.4
Repair Systems  & Information Group    
Restructuring Reserve [Roll Forward]    
Restructuring reserve, beginning balance 3.8 0.0
Provision 0.0 5.2
Usage (1.4) (1.4)
Restructuring reserve, ending balance $ 2.4 $ 3.8