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Angle
Turns to Radians
Convert turns (tr) to radians (rad). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 tr = 6.2832 rad
Turns to Radians Conversion Table
Common values, ready to copy:
| turns | radians |
|---|---|
| 1 tr | 6.2832 rad |
| 2 tr | 12.5664 rad |
| 5 tr | 31.4159 rad |
| 10 tr | 62.8319 rad |
| 25 tr | 157.08 rad |
| 50 tr | 314.16 rad |
| 100 tr | 628.32 rad |
| 1,000 tr | 6283.19 rad |
Formula
radians = turns × 6.28318531e+0
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 Turns and 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.
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.
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 radians = turns × 6.28318531e+0, 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 turns and radians 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.