Convert turns to radians
1 turn = 6.283185 rad. Change the amount below, or read the formula and the reference table further down.
1 turn equals
radians
1 turn = 6.283185 rad
The formula
Turns and radians both measure angle from the same zero, so a single multiplier does the job.
rad = turn × 6.28318531
Going the other way? Convert radians to turns.
Turns to radians table
Common values, rounded for reading.
| Turns (turn) | Radians (rad) |
|---|---|
| 1 | 6.2832 |
| 2 | 12.5664 |
| 3 | 18.8496 |
| 4 | 25.1327 |
| 5 | 31.4159 |
| 6 | 37.6991 |
| 7 | 43.9823 |
| 8 | 50.2655 |
| 9 | 56.5487 |
| 10 | 62.8319 |
| 15 | 94.2478 |
| 20 | 125.66 |
| 25 | 157.08 |
| 30 | 188.5 |
| 40 | 251.33 |
| 50 | 314.16 |
| 75 | 471.24 |
| 100 | 628.32 |
| 250 | 1,570.8 |
| 500 | 3,141.59 |
| 1,000 | 6,283.19 |
Questions people ask
- How many radians are in a turn?
- One turn equals 6.28318531 radians.
- How do I convert turns to radians by hand?
- Multiply the number of turns by 6.28318531. For a rough check, 6.3 is close enough for most everyday use.
- What is 1 turn in radians?
- 1 turn is 6.283185 radians.
Calcuit generates this page from a unit table, so the factors here match every other page on the site.