Summary of Significant Accounting Policies (Net Income Per Common Share) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 01, 2017	Oct. 02, 2016	Jul. 03, 2016	Apr. 03, 2016	Jan. 03, 2016	Sep. 27, 2015	Jun. 28, 2015	Mar. 29, 2015	Jan. 01, 2017	Jan. 03, 2016	Dec. 28, 2014
Net Income Per Common Share:
Net income attributable to Teledyne	$ 53.0	$ 52.0	$ 46.9	$ 39.0	$ 55.5	$ 48.3	$ 48.3	$ 43.7	$ 190.9	$ 195.8	$ 217.7
Basic earnings per common share
Basic earnings per common share (in USD per share)	$ 1.52	$ 1.50	$ 1.36	$ 1.13	$ 1.59	$ 1.37	$ 1.37	$ 1.22	$ 5.52	$ 5.55	$ 5.87
Diluted earnings per share:
Weighted average common shares outstanding (in shares)									34,600,000	35,300,000	37,100,000
Effect of diluted securities (in shares)									900,000	700,000	800,000
Weighted average diluted common shares outstanding (in shares)									35,500,000	36,000,000	37,900,000
Diluted earnings per common share
Diluted earnings per common share (in USD per share)	$ 1.48	$ 1.46	$ 1.33	$ 1.11	$ 1.57	$ 1.34	$ 1.34	$ 1.20	$ 5.37	$ 5.44	$ 5.75
Class of Stock [Line Items]
Shares excluded from computation of diluted earnings per share (in shares)									0		0
Stock options to purchase common stock (in shares)									2,200,000	2,400,000	2,900,000
Employee and non-employee stock option
Class of Stock [Line Items]
Shares excluded from computation of diluted earnings per share (in shares)									0	0	0
Restricted stock and performance unit
Class of Stock [Line Items]
Shares excluded from computation of diluted earnings per share (in shares)										3,997