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Angle
Radians to Turns
Convert radians (rad) to turns (tr). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 rad = 0.159155 tr
Radians to Turns Conversion Table
Common values, ready to copy:
| radians | turns |
|---|---|
| 1 rad | 0.159155 tr |
| 2 rad | 0.31831 tr |
| 5 rad | 0.795775 tr |
| 10 rad | 1.5915 tr |
| 25 rad | 3.9789 tr |
| 50 rad | 7.9577 tr |
| 100 rad | 15.9155 tr |
| 1,000 rad | 159.15 tr |
Formula
turns = radians × 1.59154943e-1
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Radians and Turns
Radians (rad): The natural SI unit for angle; one radian is the angle subtended by an arc equal in length to the radius (so a full circle is 2π radians ≈ 6.283). Common uses: Mathematics (calculus, trigonometry derivatives), physics, computer graphics, and any context where the formula simplifies in radians.
Turns (tr): A full revolution; the most natural way to describe rotation (one turn = 360° = 2π rad = 400 gon). Common uses: Engineering specifications for rotation (number of turns of a bolt, a screw thread, or a knob), and clear communication when degree confusion is a risk.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is turns = radians × 1.59154943e-1, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between radians and turns comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.