Exit and Disposal Activities - Summary of Exit and Disposal Activities (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended	12 Months Ended
	Jun. 27, 2020	Jun. 27, 2020	Jan. 02, 2021
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	$ 4.0	$ 11.5
Forecast
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs			$ 9.3
Commercial & Industrial Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	2.0	6.4
Repair Systems & Information Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	1.4	4.5
Snap-on Tools Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	0.6	0.6
Cost of goods sold:
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	2.0	7.1
Cost of goods sold: | Commercial & Industrial Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	2.0	6.4
Cost of goods sold: | Repair Systems & Information Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	0.0	0.7
Operating Expenses:
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	2.0	4.4
Operating Expenses: | Repair Systems & Information Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	1.4	3.8
Operating Expenses: | Snap-on Tools Group
Restructuring Cost and Reserve [Line Items]
Exit and disposal costs	$ 0.6	$ 0.6