Segments - Assets by Segment (Detail) - USD ($) $ in Millions	Jan. 01, 2022	Jan. 02, 2021
Segment Reporting Information [Line Items]
Assets	$ 6,759.7	$ 6,557.3
Operating Segments
Segment Reporting Information [Line Items]
Assets	5,788.6	5,555.7
Operating Segments | Commercial & Industrial Group
Segment Reporting Information [Line Items]
Assets	1,209.3	1,210.4
Operating Segments | Snap-on Tools Group
Segment Reporting Information [Line Items]
Assets	791.4	775.3
Operating Segments | Repair Systems  & Information Group
Segment Reporting Information [Line Items]
Assets	1,624.3	1,399.7
Operating Segments | Financial Services
Segment Reporting Information [Line Items]
Assets	2,163.6	2,170.3
Corporate
Segment Reporting Information [Line Items]
Assets	1,039.7	1,063.2
Intersegment eliminations
Segment Reporting Information [Line Items]
Assets	$ (68.6)	$ (61.6)