Revenue Recognition - Revenue Disaggregation (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Disaggregation of Revenue [Line Items]
Revenue from contracts with customers	$ 4,228.3	$ 3,569.3
Net sales	4,601.7	3,942.2	$ 4,067.7
Europe
Disaggregation of Revenue [Line Items]
Net sales	808.5	677.5	730.3
Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	1,406.3	1,234.6
Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	1,938.6	1,643.9
Repair Systems  & Information Group
Disaggregation of Revenue [Line Items]
Net sales	1,503.1	1,238.2
Financial Services
Disaggregation of Revenue [Line Items]
Net sales	349.7	349.7
Intersegment eliminations
Disaggregation of Revenue [Line Items]
Net sales	(596.0)	(524.2)
Product and Service, Other
Disaggregation of Revenue [Line Items]
Net sales	23.7	23.2
Product And Services, Excluding Financial Services
Disaggregation of Revenue [Line Items]
Net sales	4,252.0	3,592.5	3,730.0
Product And Services, Excluding Financial Services | Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	3,256.3	2,728.3
Product And Services, Excluding Financial Services | All other professionals
Disaggregation of Revenue [Line Items]
Net sales	995.7	864.2
Product And Services, Excluding Financial Services | North America
Disaggregation of Revenue [Line Items]
Net sales	3,071.0	2,595.8
Product And Services, Excluding Financial Services | Europe
Disaggregation of Revenue [Line Items]
Net sales	739.9	616.8
Product And Services, Excluding Financial Services | All other
Disaggregation of Revenue [Line Items]
Net sales	441.1	379.9
Product And Services, Excluding Financial Services | Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	1,095.6	951.4
Product And Services, Excluding Financial Services | Commercial & Industrial Group | Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	99.9	87.2
Product And Services, Excluding Financial Services | Commercial & Industrial Group | All other professionals
Disaggregation of Revenue [Line Items]
Net sales	995.7	864.2
Product And Services, Excluding Financial Services | Commercial & Industrial Group | North America
Disaggregation of Revenue [Line Items]
Net sales	494.9	432.3
Product And Services, Excluding Financial Services | Commercial & Industrial Group | Europe
Disaggregation of Revenue [Line Items]
Net sales	325.5	276.2
Product And Services, Excluding Financial Services | Commercial & Industrial Group | All other
Disaggregation of Revenue [Line Items]
Net sales	275.2	242.9
Product And Services, Excluding Financial Services | Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	1,938.6	1,643.9
Product And Services, Excluding Financial Services | Snap-on Tools Group | Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	1,938.6	1,643.9
Product And Services, Excluding Financial Services | Snap-on Tools Group | All other professionals
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Snap-on Tools Group | North America
Disaggregation of Revenue [Line Items]
Net sales	1,680.0	1,442.8
Product And Services, Excluding Financial Services | Snap-on Tools Group | Europe
Disaggregation of Revenue [Line Items]
Net sales	164.7	125.7
Product And Services, Excluding Financial Services | Snap-on Tools Group | All other
Disaggregation of Revenue [Line Items]
Net sales	93.9	75.4
Product And Services, Excluding Financial Services | Repair Systems  & Information Group
Disaggregation of Revenue [Line Items]
Net sales	1,217.8	997.2
Product And Services, Excluding Financial Services | Repair Systems  & Information Group | Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	1,217.8	997.2
Product And Services, Excluding Financial Services | Repair Systems  & Information Group | All other professionals
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Repair Systems  & Information Group | North America
Disaggregation of Revenue [Line Items]
Net sales	896.1	720.7
Product And Services, Excluding Financial Services | Repair Systems  & Information Group | Europe
Disaggregation of Revenue [Line Items]
Net sales	249.7	214.9
Product And Services, Excluding Financial Services | Repair Systems  & Information Group | All other
Disaggregation of Revenue [Line Items]
Net sales	72.0	61.6
Product And Services, Excluding Financial Services | Financial Services
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Financial Services | Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Financial Services | All other professionals
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Financial Services | North America
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Financial Services | Europe
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Financial Services | All other
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Intersegment eliminations
Disaggregation of Revenue [Line Items]
Net sales	(596.0)	(524.2)	(563.1)
Product And Services, Excluding Financial Services | Intersegment eliminations | Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	310.7	283.2
Product And Services, Excluding Financial Services | Intersegment eliminations | Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Intersegment eliminations | Repair Systems  & Information Group
Disaggregation of Revenue [Line Items]
Net sales	285.3	241.0
Product And Services, Excluding Financial Services | Intersegment eliminations | Financial Services
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	4,848.0	4,116.7	4,293.1
Product And Services, Excluding Financial Services | Operating Segments | Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	1,406.3	1,234.6	1,345.7
Product And Services, Excluding Financial Services | Operating Segments | Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	1,938.6	1,643.9	1,612.9
Product And Services, Excluding Financial Services | Operating Segments | Repair Systems  & Information Group
Disaggregation of Revenue [Line Items]
Net sales	1,503.1	1,238.2	1,334.5
Product And Services, Excluding Financial Services | Operating Segments | Financial Services
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Financial Service
Disaggregation of Revenue [Line Items]
Net sales	349.7	349.7	$ 337.7
Financial Service | Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Financial Service | Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Financial Service | Repair Systems  & Information Group
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0
Financial Service | Financial Services
Disaggregation of Revenue [Line Items]
Net sales	$ 349.7	$ 349.7