Segments - Products and Services (Detail) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Revenue from External Customer [Line Items]
Net sales	$ 4,601.7	$ 3,942.2	$ 4,067.7
Product And Services, Excluding Financial Services
Revenue from External Customer [Line Items]
Net sales	4,252.0	3,592.5	3,730.0
Product And Services, Excluding Financial Services | Tools
Revenue from External Customer [Line Items]
Net sales	2,343.0	1,984.7	2,017.5
Product And Services, Excluding Financial Services | Diagnostics, information and management systems
Revenue from External Customer [Line Items]
Net sales	892.5	783.8	827.5
Product And Services, Excluding Financial Services | Equipment
Revenue from External Customer [Line Items]
Net sales	1,016.5	824.0	885.0
Financial Services
Revenue from External Customer [Line Items]
Net sales	$ 349.7	$ 349.7	$ 337.7