Turns to Radians
Convert turns to radians (turns to rad). 1 turns = 6.28318530718 rad. Use the calculator, formula and conversion table.
How to convert turns to radians
Multiply the amount in turns by 6.28318530718 to get radians. The displayed factor and results are rounded to 12 significant digits.
rad = turns × 6.28318530718Worked example
1 turns = 6.28318530718 rad. Change the amount in the calculator above to use your own value.
Units and assumptions
A full turn is 360 degrees, 2π radians or 400 gradians. Angles are converted without wrapping, so values above one turn and negative angles are retained.
Calculator results use floating-point arithmetic and are rounded for display. The reference table below uses up to 12 significant digits.
Turns to Radians table
| Turns (turns) | Radians (rad) |
|---|---|
| 0 | 0 |
| 1 | 6.28318530718 |
| 5 | 31.4159265359 |
| 10 | 62.8318530718 |
| 25 | 157.079632679 |
| 100 | 628.318530718 |
| 1,000 | 6,283.18530718 |
About this conversion
What is the formula for turns to radians?
rad = turns × 6.28318530718. Multiply the amount in turns by 6.28318530718 to get radians. The displayed factor and results are rounded to 12 significant digits.
How do I convert back to turns?
Use the radians to turns calculator to reverse this conversion. You can also use Swap units in the calculator above.
Can I use a different pair of units?
Choose another unit in the calculator, or open the angle converter to browse all supported pairs.