Convert Turns to Radians
1 turn = 6.283185 radians. Type any value below to convert in either direction — the calculation happens in your browser.
Turns to Radians formula
Multiply the number of turns by 6.283185 to get radians.
radians = turns × 6.283185To go the other way: divide the number of radians by 6.283185, or multiply by 0.1591549.
turns = radians ÷ 6.283185Turns to Radians conversion table
| Turns | Radians |
|---|---|
| 1 turn | 6.283185 rad |
| 2 turn | 12.566371 rad |
| 3 turn | 18.849556 rad |
| 4 turn | 25.132741 rad |
| 5 turn | 31.415927 rad |
| 6 turn | 37.699112 rad |
| 7 turn | 43.982297 rad |
| 8 turn | 50.265482 rad |
| 9 turn | 56.548668 rad |
| 10 turn | 62.831853 rad |
| 15 turn | 94.24778 rad |
| 20 turn | 125.663706 rad |
| 25 turn | 157.079633 rad |
| 30 turn | 188.495559 rad |
| 40 turn | 251.327412 rad |
| 50 turn | 314.159265 rad |
| 75 turn | 471.238898 rad |
| 100 turn | 628.318531 rad |
| 250 turn | 1,570.796 rad |
| 500 turn | 3,141.593 rad |
| 1,000 turn | 6,283.185 rad |
Radians to Turns conversion table
| Radians | Turns |
|---|---|
| 1 rad | 0.1591549 turn |
| 2 rad | 0.3183099 turn |
| 3 rad | 0.4774648 turn |
| 4 rad | 0.6366198 turn |
| 5 rad | 0.7957747 turn |
| 6 rad | 0.9549297 turn |
| 7 rad | 1.114085 turn |
| 8 rad | 1.27324 turn |
| 9 rad | 1.432394 turn |
| 10 rad | 1.591549 turn |
About the turn
A turn is one complete revolution, equal to 360 degrees or 2π radians.
About the radian
A radian is the angle subtending an arc equal to the radius; a full turn is 2π radians.
Frequently asked questions
How many radians are in a turn?
There are 6.283185 radians in one turn.
How many turns are in a radian?
There are 0.1591549 turns in one radian.
Is this conversion exact?
The ratio between the turn and the radian is fixed by definition, so the conversion is exact — the figures shown here are rounded for readability only.
What is 10 turns in radians?
10 turns equals 62.831853 radians.