Revenue Recognition - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Contract with customer, liability	$ 63.8	$ 61.0
Contract with customer, liability, revenue recognized	$ 52.3
Software Subscriptions, Extended Warranties and Other Subscription Agreements
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue, performance obligation, description of timing	For performance obligations related to software subscriptions, extended warranties and other subscription agreements, Snap-on transfers control and recognizes revenue over time on a ratable basis using a time-based output method. The performance obligations are typically satisfied as services are rendered on a straight-line basis over the contract term, which is generally for 12 months but can be for a term up to 60 months.
Franchise Fee Revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue from contract with customer	$ 17.3	$ 16.2	$ 15.4
Ship-and-Bill Type Contracts
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue, performance obligation, description of timing	For ship-and-bill type contracts with customers, the contract states the final terms of the sale, including the description, quantity, and price of each product or service purchased. Payment terms are typically due upon delivery or up to 30 days after delivery but can range up to 120 days after delivery.
Subscription Contracts
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue, performance obligation, description of timing	For subscription contracts, payment terms are in advance or in arrears of services on a monthly, quarterly or annual basis over the contract term, which is generally for 12 months but can be for a term up to 60 months depending on the product or service.
Transferred at Point in Time | Sales Revenue Net | Product Concentration Risk
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Concentration risk, percentage	90.00%