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. 01, 2016	Oct. 02, 2015	Jul. 03, 2015	Apr. 03, 2015	Jan. 02, 2015	Oct. 03, 2014	Jul. 04, 2014	Apr. 04, 2014	Jan. 01, 2016	Jan. 02, 2015	Jan. 03, 2014
Net income attributable to Trimble Navigation Limited	$ 24.0	$ 37.1	$ 25.9	$ 34.1	$ 55.8	$ 11.8	$ 77.9	$ 68.6	$ 121.1	$ 214.1	$ 218.9
Weighted average number of common shares used in basic earnings per share									255.8	260.1	256.6
Effect of dilutive securities									2.7	4.4	4.6
Weighted average number of common shares and dilutive potential common shares used in diluted earnings per share									258.5	264.5	261.2
Basic earnings per share	$ 0.10	$ 0.15	$ 0.10	$ 0.13	$ 0.22	$ 0.05	$ 0.30	$ 0.26	$ 0.47	$ 0.82	$ 0.85
Diluted earnings per share	$ 0.09	$ 0.14	$ 0.10	$ 0.13	$ 0.21	$ 0.04	$ 0.29	$ 0.26	$ 0.47	$ 0.81	$ 0.84