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Segments - Net Sales by Segment (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Segment Reporting Information [Line Items]
Net sales	$ 4,842.5	$ 4,601.7	$ 3,942.2
Operating earnings	1,207.2	1,123.5	880.5
Interest expense	(47.1)	(53.1)	(54.0)
Other income (expense) – net	42.5	16.5	8.7
Earnings before income taxes and equity earnings	1,202.6	1,086.9	835.2
Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales	1,399.2	1,406.3
Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales	2,072.0	1,938.6
Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales	1,666.9	1,503.1
Financial Services
Segment Reporting Information [Line Items]
Net sales	349.7	349.7
Operating Segments
Segment Reporting Information [Line Items]
Operating earnings	1,315.6	1,241.6	968.0
Operating Segments \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Operating earnings	197.6	209.9	153.7
Operating Segments \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Operating earnings	458.7	411.1	267.7
Operating Segments \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Operating earnings	393.3	348.6	298.0
Operating Segments \| Financial Services
Segment Reporting Information [Line Items]
Operating earnings	266.0	272.0	248.6
Intersegment eliminations
Segment Reporting Information [Line Items]
Net sales	(645.3)	(596.0)
Corporate
Segment Reporting Information [Line Items]
Operating earnings	(108.4)	(118.1)	(87.5)
Product And Services, Excluding Financial Services
Segment Reporting Information [Line Items]
Net sales	4,492.8	4,252.0	3,592.5
Operating earnings	941.2	851.5	631.9
Product And Services, Excluding Financial Services \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales	1,058.3	1,095.6
Product And Services, Excluding Financial Services \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales	2,072.0	1,938.6
Product And Services, Excluding Financial Services \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales	1,362.5	1,217.8
Product And Services, Excluding Financial Services \| Financial Services
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services \| Operating Segments
Segment Reporting Information [Line Items]
Net sales	5,138.1	4,848.0	4,116.7
Product And Services, Excluding Financial Services \| Operating Segments \| Commercial & Industrial Group
Segment Reporting Information [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
Segment Reporting Information [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
Segment Reporting Information [Line Items]
Net sales	1,666.9	1,503.1	1,238.2
Product And Services, Excluding Financial Services \| Operating Segments \| Financial Services
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services \| Intersegment eliminations
Segment Reporting Information [Line Items]
Net sales	(645.3)	(596.0)	(524.2)
Product And Services, Excluding Financial Services \| Intersegment eliminations \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales	340.9	310.7
Product And Services, Excluding Financial Services \| Intersegment eliminations \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Product And Services, Excluding Financial Services \| Intersegment eliminations \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales	304.4	285.3
Product And Services, Excluding Financial Services \| Intersegment eliminations \| Financial Services
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Financial Service
Segment Reporting Information [Line Items]
Net sales	349.7	349.7	349.7
Operating earnings	266.0	272.0	$ 248.6
Financial Service \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Financial Service \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Financial Service \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Financial Service \| Financial Services
Segment Reporting Information [Line Items]
Net sales	$ 349.7	$ 349.7