Earnings Per Share (Schedule Of Computation Of Earnings Per Share And Effect On Weighted-Average Number Of Shares) (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 03, 2020	Sep. 27, 2019	Jun. 28, 2019	Mar. 29, 2019	Dec. 28, 2018	Sep. 28, 2018	Jun. 29, 2018	Mar. 30, 2018	Jan. 03, 2020	Dec. 28, 2018	Dec. 29, 2017
Net income attributable to Trimble Inc.	$ 279.3	$ 78.1	$ 94.6	$ 62.3	$ 86.5	$ 73.7	$ 64.1	$ 58.5	$ 514.3	$ 282.8	$ 118.4
Weighted average number of common shares used in basic earnings per share									250.8	250.0	252.1
Effect of dilutive securities									2.1	3.4	4.6
Weighted average number of common shares and dilutive potential common shares used in diluted earnings per share									252.9	253.4	256.7
Basic earnings per share	$ 1.12	$ 0.31	$ 0.38	$ 0.25	$ 0.34	$ 0.29	$ 0.26	$ 0.24	$ 2.05	$ 1.13	$ 0.47
Diluted earnings per share	$ 1.11	$ 0.31	$ 0.37	$ 0.25	$ 0.34	$ 0.29	$ 0.25	$ 0.23	$ 2.03	$ 1.12	$ 0.46