Turns to Radians
Convert turns (turn) to radians (rad). Type in either box; the other updates as you go.
1 turn equals6.283185307 rad
1 radian equals0.1591549431 turn
Formularad = turn × 6.283185307
How to convert turns to radians
To convert turns to radians, multiply the number of turns by 6.283185307.
rad = turn × 6.283185307
Example
Convert 5 turns to radians:
5 turn × 6.283185307 = 31.4159 rad
Turn to radian conversion chart
| Turns (turn) | Radians (rad) |
|---|---|
| 1 turn | 6.283185 rad |
| 2 turn | 12.56637 rad |
| 3 turn | 18.84956 rad |
| 4 turn | 25.13274 rad |
| 5 turn | 31.41593 rad |
| 6 turn | 37.69911 rad |
| 7 turn | 43.9823 rad |
| 8 turn | 50.26548 rad |
| 9 turn | 56.54867 rad |
| 10 turn | 62.83185 rad |
| 12 turn | 75.39822 rad |
| 15 turn | 94.24778 rad |
| 20 turn | 125.6637 rad |
| 25 turn | 157.0796 rad |
| 30 turn | 188.4956 rad |
| 40 turn | 251.3274 rad |
| 50 turn | 314.1593 rad |
| 60 turn | 376.9911 rad |
| 70 turn | 439.823 rad |
| 75 turn | 471.2389 rad |
| 80 turn | 502.6548 rad |
| 90 turn | 565.4867 rad |
| 100 turn | 628.3185 rad |
| 150 turn | 942.4778 rad |
| 200 turn | 1,256.637 rad |
| 250 turn | 1,570.796 rad |
| 500 turn | 3,141.593 rad |
| 1,000 turn | 6,283.185 rad |
Going the other way? See the radians to turns chart.
About the units
Turn (turn)
A turn is one full revolution, 360 degrees or 2π radians.
Radian (rad)
A radian is the angle that cuts off an arc as long as the radius. A full turn is 2π radians, so one radian is about 57.3°.
Frequently asked questions
How many radians are in a turn?
There are 6.283185307 radians in a turn.
How many turns are in a radian?
There are 0.1591549431 turns in a radian.
How do you convert turns to radians?
To convert turns to radians, multiply the number of turns by 6.283185307.
What is 5 turns in radians?
5 turns equals 31.4159 radians.
Convert between degrees, radians, gradians, arcminutes and arcseconds. Open the angle converter to see a value in every unit at once.