Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill by Segment (Details) $ in Millions	9 Months Ended
	Oct. 01, 2022 USD ($)
Goodwill [Roll Forward]
Balance as of January 1, 2022	$ 1,116.5
Currency translation	(72.8)
Acquisition-related adjustments	(33.1)
Balance as of July 2, 2022	1,010.6
Commercial & Industrial Group
Goodwill [Roll Forward]
Balance as of January 1, 2022	325.8
Currency translation	(44.6)
Acquisition-related adjustments	(0.5)
Balance as of July 2, 2022	280.7
Snap-on Tools Group
Goodwill [Roll Forward]
Balance as of January 1, 2022	12.4
Currency translation	0.0
Acquisition-related adjustments	0.0
Balance as of July 2, 2022	12.4
Repair Systems & Information Group
Goodwill [Roll Forward]
Balance as of January 1, 2022	778.3
Currency translation	(28.2)
Acquisition-related adjustments	(32.6)
Balance as of July 2, 2022	$ 717.5