Turns to radians converter
Radians (rad)
1 turn = 6.283185307 radians
How to convert turns to radians
rad = tr × 6.28318530718
Multiply the number of turns by 6.28318530718 to get radians. Going the other way, divide by 6.28318530718 (or multiply by 0.159154943092).
One turn is exactly defined as 6.28318530718 radians (to 12 significant figures), and one radian is 0.159154943092 turns.
Worked examples
- Convert 5 turns: 5 × 6.28318530718 = 31.41592654 31.41592654 radians.
- Convert 12.5 turns: 12.5 × 6.28318530718 = 78.53981634 78.53981634 radians.
- Convert 250 turns: 250 × 6.28318530718 = 1,570.796327 1,570.796327 radians.
Quick-reference table
| tr | rad |
|---|---|
| 1 | 6.283185307 |
| 2 | 12.56637061 |
| 3 | 18.84955592 |
| 5 | 31.41592654 |
| 10 | 62.83185307 |
| 15 | 94.24777961 |
| 20 | 125.6637061 |
| 25 | 157.0796327 |
| 50 | 314.1592654 |
| 75 | 471.238898 |
| 100 | 628.3185307 |
| 1,000 | 6,283.185307 |
| rad | tr |
|---|---|
| 1 | 0.1591549431 |
| 2 | 0.3183098862 |
| 3 | 0.4774648293 |
| 5 | 0.7957747155 |
| 10 | 1.591549431 |
| 15 | 2.387324146 |
| 20 | 3.183098862 |
| 25 | 3.978873577 |
| 50 | 7.957747155 |
| 75 | 11.93662073 |
| 100 | 15.91549431 |
| 1,000 | 159.1549431 |
Related conversions
Frequently asked questions
How many radians are in 1 turn?
1 turn equals 6.283185307 radians.
What is the formula to convert turns to radians?
Use rad = tr × 6.28318530718. Multiply the number of turns by 6.28318530718 to get radians. Going the other way, divide by 6.28318530718 (or multiply by 0.159154943092).
What is 100 turns in radians?
100 turns is 628.3185307 radians.