Radians to turns – convert rad to turn
Convert radians to turns (rad to turn) to express angles as a fraction of a full revolution instead of in pure radians. This page opens the main angle converter with rad → turn pre-selected.
Open the interactive radians → turns converter:
Use main converter (rad → turn) or switch to turns → radiansThe angle converter also supports degrees (°) and gradians (gon) for maths, surveying and graphics work.
Quick reference: radians to turns
One full turn is 2π radians, so a single radian is 1 / (2π) ≈ 0.15915 turns. The formula is: turns = radians ÷ (2π).
| Angle (rad) | Angle (turn, approx.) |
|---|---|
| π/6 ≈ 0.524 | 0.0833 turn |
| π/4 ≈ 0.785 | 0.1250 turn |
| π/3 ≈ 1.047 | 0.1667 turn |
| π/2 ≈ 1.571 | 0.25 turn |
| π ≈ 3.142 | 0.5 turn |
| 2π ≈ 6.283 | 1.0 turn |
Why convert radians to turns?
Radians to turns is useful when you:
- Describe rotor or wheel position as a fraction of a full revolution.
- Configure animations or CSS transforms that accept turns as a unit.
- Work with control systems where a motor’s range is expressed in turns.
- Teach the relationship between radians, degrees and full rotations.
Other angle converters on this site
Turns are often written as “rotations” or “revolutions”. 0.25 turn is a quarter turn, 0.5 turn is a half turn and 1 turn is a complete circle.
Page last updated: 4 December 2025.