Exit and Disposal Activities - Accrual Activity (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
	Oct. 01, 2022	Jul. 02, 2022
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	$ 5.4	$ 7.0
Provision	0.0	0.0
Usage	(1.6)	(1.6)
Restructuring reserve, ending balance	3.8	5.4
Commercial & Industrial Group
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	3.4	4.3
Provision	0.0	0.0
Usage	(0.9)	(0.9)
Restructuring reserve, ending balance	2.5	3.4
Snap-on Tools Group
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	0.3	0.3
Provision	0.0	0.0
Usage	(0.2)	0.0
Restructuring reserve, ending balance	0.1	0.3
Repair Systems & Information Group
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	1.7	2.4
Provision	0.0	0.0
Usage	(0.5)	(0.7)
Restructuring reserve, ending balance	$ 1.2	$ 1.7