How to convert turns to radians
rad = tr × 6.283185307Multiply the value in turns by 6.283185307. To go the other way, multiply by 0.1591549431 (or divide by 6.283185307).
A turn is larger than a radian: one turn contains 6.283185307 radians.
Worked examples
- 1 turn (revolution)1 tr × 6.283185307 = 6.283185307 rad
- 5 turns5 tr × 6.283185307 = 31.41592654 rad
- 10 turns10 tr × 6.283185307 = 62.83185307 rad
- 20 turns20 tr × 6.283185307 = 125.6637061 rad
- 100 turns100 tr × 6.283185307 = 628.3185307 rad
Turns to radians conversion table
Values are calculated by the conversion engine and rounded to 8 significant figures.
| Turns (tr) | Radians (rad) |
|---|---|
| 0.1 tr | 0.62831853 rad |
| 0.25 tr | 1.5707963 rad |
| 0.5 tr | 3.1415927 rad |
| 1 tr | 6.2831853 rad |
| 2 tr | 12.566371 rad |
| 3 tr | 18.849556 rad |
| 4 tr | 25.132741 rad |
| 5 tr | 31.415927 rad |
| 6 tr | 37.699112 rad |
| 7 tr | 43.982297 rad |
| 8 tr | 50.265482 rad |
| 9 tr | 56.548668 rad |
| 10 tr | 62.831853 rad |
| Turns (tr) | Radians (rad) |
|---|---|
| 12 tr | 75.398224 rad |
| 15 tr | 94.24778 rad |
| 20 tr | 125.66371 rad |
| 25 tr | 157.07963 rad |
| 30 tr | 188.49556 rad |
| 40 tr | 251.32741 rad |
| 50 tr | 314.15927 rad |
| 75 tr | 471.2389 rad |
| 100 tr | 628.31853 rad |
| 250 tr | 1,570.7963 rad |
| 500 tr | 3,141.5927 rad |
| 1,000 tr | 6,283.1853 rad |
About the units
Turn (tr)
The turn (tr) is a unit of angle. One turn equals 6.283185307 radians (rad).
Radian (rad)
The angle subtended by an arc equal in length to the radius; 2π rad make a full turn, so 1 rad ≈ 57.2958°.
Frequently asked questions
How many radians are in one turn?
There are 6.283185307 radians in one turn, and this value is exact by definition.
How do I convert turns to radians?
Multiply the number of turns by 6.283185307. For example, 10 tr × 6.283185307 = 62.83185307 rad.
How many turns are in one radian?
One radian equals 0.1591549431 turns. That is the reverse factor, 1 ÷ 6.283185307.
What is 10 turns in radians?
10 tr = 62.83185307 rad.
Is this tr to rad converter accurate?
Yes. Both units are defined exactly in terms of SI units, so the conversion factor is exact; results are shown to 12 significant figures by default and you can change precision in the converter. Calculations run in your browser using the same tested engine that generated this page.