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
	Dec. 30, 2016	Sep. 30, 2016	Jul. 01, 2016	Apr. 01, 2016	Jan. 01, 2016	Oct. 02, 2015	Jul. 03, 2015	Apr. 03, 2015	Dec. 30, 2016	Jan. 01, 2016	Jan. 02, 2015
Net income attributable to Trimble Inc.	$ 37.7	$ 39.2	$ 35.7	$ 19.8	$ 24.0	$ 37.1	$ 25.9	$ 34.1	$ 132.4	$ 121.1	$ 214.1
Weighted average number of common shares used in basic earnings per share									250.5	255.8	260.1
Effect of dilutive securities									3.4	2.7	4.4
Weighted average number of common shares and dilutive potential common shares used in diluted earnings per share									253.9	258.5	264.5
Basic earnings per share	$ 0.15	$ 0.16	$ 0.14	$ 0.08	$ 0.10	$ 0.15	$ 0.10	$ 0.13	$ 0.53	$ 0.47	$ 0.82
Diluted earnings per share	$ 0.15	$ 0.15	$ 0.14	$ 0.08	$ 0.09	$ 0.14	$ 0.10	$ 0.13	$ 0.52	$ 0.47	$ 0.81