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Segments - Net Sales by Segment (Detail) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 02, 2021	Sep. 26, 2020	Jun. 27, 2020	Mar. 28, 2020	Dec. 28, 2019	Sep. 28, 2019	Jun. 29, 2019	Mar. 30, 2019	Jan. 02, 2021	Dec. 28, 2019	Dec. 29, 2018
Segment Reporting Information [Line Items]
Net sales									$ 3,942.2	$ 4,067.7	$ 4,070.4
Operating earnings									880.5	962.3	956.1
Interest expense									(54.0)	(49.0)	(50.4)
Other income (expense) – net									8.7	8.8	4.2
Earnings before income taxes and equity earnings									835.2	922.1	909.9
Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales									1,234.6	1,345.7
Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales									1,643.9	1,612.9
Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales									1,238.2	1,334.5
Financial Services
Segment Reporting Information [Line Items]
Net sales									349.7	337.7
Operating Segments
Segment Reporting Information [Line Items]
Operating earnings									968.0	1,023.1	1,036.2
Operating Segments \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Operating earnings									153.7	188.7	199.3
Operating Segments \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Operating earnings									267.7	245.8	264.2
Operating Segments \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Operating earnings									298.0	342.7	342.6
Operating Segments \| Financial Services
Segment Reporting Information [Line Items]
Operating earnings									248.6	245.9	230.1
Intersegment eliminations
Segment Reporting Information [Line Items]
Net sales									(524.2)	(563.1)
Corporate
Segment Reporting Information [Line Items]
Operating earnings									(87.5)	(60.8)	(80.1)
Product And Services, Excluding Financial Services
Segment Reporting Information [Line Items]
Net sales	$ 1,074.4	$ 941.6	$ 724.3	$ 852.2	$ 955.2	$ 901.8	$ 951.3	$ 921.7	3,592.5	3,730.0	3,740.7
Operating earnings									631.9	716.4	726.0
Product And Services, Excluding Financial Services \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales									951.4	1,038.2
Product And Services, Excluding Financial Services \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales									1,643.9	1,612.9
Product And Services, Excluding Financial Services \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales									997.2	1,078.9
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									4,116.7	4,293.1	4,291.5
Product And Services, Excluding Financial Services \| Operating Segments \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales									1,234.6	1,345.7	1,343.3
Product And Services, Excluding Financial Services \| Operating Segments \| Snap-on Tools Group
Segment Reporting Information [Line Items]
Net sales									1,643.9	1,612.9	1,613.8
Product And Services, Excluding Financial Services \| Operating Segments \| Repair Systems & Information Group
Segment Reporting Information [Line Items]
Net sales									1,238.2	1,334.5	1,334.4
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									(524.2)	(563.1)	(550.8)
Product And Services, Excluding Financial Services \| Intersegment eliminations \| Commercial & Industrial Group
Segment Reporting Information [Line Items]
Net sales									283.2	307.5
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									241.0	255.6
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	$ 93.4	$ 85.8	$ 84.6	$ 85.9	$ 83.9	$ 84.1	$ 84.1	$ 85.6	349.7	337.7	329.7
Operating earnings									248.6	245.9	$ 230.1
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	$ 337.7