Revenue Recognition - Revenue Disaggregation (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Disaggregation of Revenue [Line Items]
Revenue from contracts with customers	$ 4,468.6	$ 4,228.3
Net sales	4,842.5	4,601.7	$ 3,942.2
Europe
Disaggregation of Revenue [Line Items]
Net sales	723.3	808.5	677.5
Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	1,399.2	1,406.3
Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	2,072.0	1,938.6
Repair Systems & Information Group
Disaggregation of Revenue [Line Items]
Net sales	1,666.9	1,503.1
Financial Services
Disaggregation of Revenue [Line Items]
Net sales	349.7	349.7
Intersegment eliminations
Disaggregation of Revenue [Line Items]
Net sales	(645.3)	(596.0)
Product and Service, Other
Disaggregation of Revenue [Line Items]
Net sales	24.2	23.7
Product And Services, Excluding Financial Services
Disaggregation of Revenue [Line Items]
Net sales	4,492.8	4,252.0	3,592.5
Product And Services, Excluding Financial Services \| Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	3,525.3	3,256.3
Product And Services, Excluding Financial Services \| All other professionals
Disaggregation of Revenue [Line Items]
Net sales	967.5	995.7
Product And Services, Excluding Financial Services \| North America
Disaggregation of Revenue [Line Items]
Net sales	3,384.7	3,071.0
Product And Services, Excluding Financial Services \| Europe
Disaggregation of Revenue [Line Items]
Net sales	650.3	739.9
Product And Services, Excluding Financial Services \| All other
Disaggregation of Revenue [Line Items]
Net sales	457.8	441.1
Product And Services, Excluding Financial Services \| Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	1,058.3	1,095.6
Product And Services, Excluding Financial Services \| Commercial & Industrial Group \| Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	90.8	99.9
Product And Services, Excluding Financial Services \| Commercial & Industrial Group \| All other professionals
Disaggregation of Revenue [Line Items]
Net sales	967.5	995.7
Product And Services, Excluding Financial Services \| Commercial & Industrial Group \| North America
Disaggregation of Revenue [Line Items]
Net sales	498.3	494.9
Product And Services, Excluding Financial Services \| Commercial & Industrial Group \| Europe
Disaggregation of Revenue [Line Items]
Net sales	284.9	325.5
Product And Services, Excluding Financial Services \| Commercial & Industrial Group \| All other
Disaggregation of Revenue [Line Items]
Net sales	275.1	275.2
Product And Services, Excluding Financial Services \| Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	2,072.0	1,938.6
Product And Services, Excluding Financial Services \| Snap-on Tools Group \| Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	2,072.0	1,938.6
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	1,840.3	1,680.0
Product And Services, Excluding Financial Services \| Snap-on Tools Group \| Europe
Disaggregation of Revenue [Line Items]
Net sales	137.9	164.7
Product And Services, Excluding Financial Services \| Snap-on Tools Group \| All other
Disaggregation of Revenue [Line Items]
Net sales	93.8	93.9
Product And Services, Excluding Financial Services \| Repair Systems & Information Group
Disaggregation of Revenue [Line Items]
Net sales	1,362.5	1,217.8
Product And Services, Excluding Financial Services \| Repair Systems & Information Group \| Vehicle service professionals
Disaggregation of Revenue [Line Items]
Net sales	1,362.5	1,217.8
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	1,046.1	896.1
Product And Services, Excluding Financial Services \| Repair Systems & Information Group \| Europe
Disaggregation of Revenue [Line Items]
Net sales	227.5	249.7
Product And Services, Excluding Financial Services \| Repair Systems & Information Group \| All other
Disaggregation of Revenue [Line Items]
Net sales	88.9	72.0
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	(645.3)	(596.0)	(524.2)
Product And Services, Excluding Financial Services \| Intersegment eliminations \| Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	340.9	310.7
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	304.4	285.3
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	5,138.1	4,848.0	4,116.7
Product And Services, Excluding Financial Services \| Operating Segments \| Commercial & Industrial Group
Disaggregation of Revenue [Line Items]
Net sales	1,399.2	1,406.3	1,234.6
Product And Services, Excluding Financial Services \| Operating Segments \| Snap-on Tools Group
Disaggregation of Revenue [Line Items]
Net sales	2,072.0	1,938.6	1,643.9
Product And Services, Excluding Financial Services \| Operating Segments \| Repair Systems & Information Group
Disaggregation of Revenue [Line Items]
Net sales	1,666.9	1,503.1	1,238.2
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	$ 349.7
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