Convert turns to radians
Input the number of turns you want to convert to radians.
How to Convert Turns to Radians
The turn and radian are both units of angle. 1 turn equals 6.2831853072 radians. This means to convert turns to radians, you multiply by 6.2831853072.
Formula
Step-by-Step Example
Convert 5 turn to radians:
We need to convert turns to radians
Since 1 turn = 6.2831853072 rad, multiply by 6.2831853072
5 × 6.2831853072 = 31.415926536
5 turn = 31.415926536 rad
Turn to Radian Conversion Table
Quick reference table for common turn to radian conversions. Click any value for detailed calculation.
| Turns (turn) | Radians (rad) |
|---|---|
| 1 turn | 6.2831853072 rad |
| 2 turn | 12.566370614 rad |
| 5 turn | 31.415926536 rad |
| 10 turn | 62.831853072 rad |
| 15 turn | 94.247779608 rad |
| 20 turn | 125.66370614 rad |
| 25 turn | 157.07963268 rad |
| 50 turn | 314.15926536 rad |
| 100 turn | 628.31853072 rad |
About These Units
Turn (turn)
A turn (revolution, cycle, or rotation) is one complete 360° rotation. Turns simplify rotational calculations: 0.5 turns = 180°, 0.25 turns = 90°. Used in engineering, dance choreography, and describing rotational motion. Also called "full rotation" or "cycle."
Radian (rad)
A radian (rad) is the SI unit of angle where the arc length equals the radius. One radian ≈ 57.3°. A full circle is 2π radians (≈6.28 rad). Radians are essential in calculus, physics, and engineering. Trigonometric functions in most programming languages use radians.
Frequently Asked Questions
How do I convert turns to radians?
To convert turns to radians, multiply the value by 6.2831853072. For example, 10 turn = 62.831853072 rad.
How many radians are in 1 turn?
1 turn equals 6.2831853072 radians.
What is the formula for turns to radians?
The formula is: rad = turn × 6.2831853072.