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Segments - Products and Services (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Revenue from External Customer [Line Items]
Net sales	$ 4,842.5	$ 4,601.7	$ 3,942.2
Product And Services, Excluding Financial Services
Revenue from External Customer [Line Items]
Net sales	4,492.8	4,252.0	3,592.5
Product And Services, Excluding Financial Services | Tools
Revenue from External Customer [Line Items]
Net sales	2,399.4	2,343.0	1,984.7
Product And Services, Excluding Financial Services | Diagnostics, information and management systems
Revenue from External Customer [Line Items]
Net sales	942.4	892.5	783.8
Product And Services, Excluding Financial Services | Equipment
Revenue from External Customer [Line Items]
Net sales	1,151.0	1,016.5	824.0
Financial Services
Revenue from External Customer [Line Items]
Net sales	$ 349.7	$ 349.7	$ 349.7

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Amount of revenue recognized from goods sold, services rendered, insurance premiums, or other activities that constitute an earning process. Includes, but is not limited to, investment and interest income before deduction of interest expense when recognized as a component of revenue, and sales and trading gain (loss).

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