Radians to Turns
An instant radians-to-turns converter, with the formula and a reference table below.
| Radians | Turns |
|---|---|
| 1 rad | 0.159155 turn |
| 2 rad | 0.31831 turn |
| 3 rad | 0.477465 turn |
| 5 rad | 0.795775 turn |
| 10 rad | 1.591549 turn |
| 25 rad | 3.978874 turn |
| 50 rad | 7.957747 turn |
| 100 rad | 15.915494 turn |
How to use
- Enter a value in the Radians field.
- The Turns figure appears immediately — no button to press.
- Typing in the Turns field converts back to Radians the same way.
- Use the reference table for the values that come up most often.
Radians to Turns formula
Converting radians to turns is a single multiplication by 0.159154943.
turn = rad × 0.159154943
Why this factor: the radian and the turn are both defined against the degree, so dividing one definition by the other gives 0.159154943 directly. Both definitions are set out in full below.
To go the other way, divide by 0.159154943 — or use the Turns to Radians converter, which is the same calculation reversed.
Worked example
Start with 30 rad. Multiply by 0.159154943 to get 4.774648 turn.
30 rad × 0.159154943 = 4.774648 turn
The converter above does this for any value you type, in either direction.
What is a radian?
A radian is the angle that subtends an arc equal in length to the circle's radius — the natural unit of angle.
Definition: A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.
Where it is used: Calculus and trigonometry, physics, and every standard programming library's sin, cos and tan.
Worth knowing: Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
What is a turn?
A turn is one complete revolution — a full circle.
Definition: Exactly 360 degrees, or 2π radians.
Where it is used: Rotational counting, gear and pulley ratios, and coil and winding specifications.
Radians vs Turns
The radian is an SI unit while the turn is a specialized unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many turns are in a radian?
One radian equals 0.159154943 turns.
What is the formula to convert radians to turns?
Multiply the number of radians by 0.159154943. To reverse it, divide by 0.159154943 instead.
How do I convert turns back to radians?
Divide by 0.159154943, which is the same as multiplying by 6.28318531.
How many turns are in 10 radians?
10 rad works out to 1.591549 turn.
Is there anything to watch out for with radians?
Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
How is the radian defined?
A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.