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Segments - Assets by Segment (Details) - USD ($) $ in Millions	Oct. 02, 2021	Jan. 02, 2021
Segment Reporting Information [Line Items]
Assets	$ 6,580.9	$ 6,557.3
Operating Segments
Segment Reporting Information [Line Items]
Assets	5,758.9	5,555.7
Operating Segments | Commercial & Industrial Group
Segment Reporting Information [Line Items]
Assets	1,213.0	1,210.4
Operating Segments | Snap-on Tools Group
Segment Reporting Information [Line Items]
Assets	763.9	775.3
Operating Segments | Repair Systems & Information Group
Segment Reporting Information [Line Items]
Assets	1,608.7	1,399.7
Operating Segments | Financial Services
Segment Reporting Information [Line Items]
Assets	2,173.3	2,170.3
Corporate
Segment Reporting Information [Line Items]
Assets	886.5	1,063.2
Elimination of intersegment receivables
Segment Reporting Information [Line Items]
Assets	$ (64.5)	$ (61.6)

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Sum of the carrying amounts as of the balance sheet date of all assets that are recognized. Assets are probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

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