Segments - Assets by Segment (Details) - USD ($) $ in Millions	Jul. 02, 2022	Jan. 01, 2022
Segment Reporting Information [Line Items]
Assets	$ 6,864.3	$ 6,759.7
Operating segments
Segment Reporting Information [Line Items]
Assets	5,841.3	5,788.6
Operating segments | Commercial & Industrial Group
Segment Reporting Information [Line Items]
Assets	1,204.6	1,209.3
Operating segments | Snap-on Tools Group
Segment Reporting Information [Line Items]
Assets	842.3	791.4
Operating segments | Repair Systems & Information Group
Segment Reporting Information [Line Items]
Assets	1,630.1	1,624.3
Operating segments | Financial Services
Segment Reporting Information [Line Items]
Assets	2,164.3	2,163.6
Corporate
Segment Reporting Information [Line Items]
Assets	1,107.8	1,039.7
Elimination of intersegment receivables
Segment Reporting Information [Line Items]
Assets	$ (84.8)	$ (68.6)