Convert Turn to Radian
Use this free converter to change turns (turn) into radians (rad). Turn and radian both measure angle. As a quick reference, 1 turn equals 6.2831853 rad, and 1 rad equals 0.15915494 turn.
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Radian (rad)
6.2831853
1 turn = 6.2831853 rad
Angle conversion table
| Turn | Radian |
|---|---|
| 0.01 | 0.062831853 |
| 0.1 | 0.62831853 |
| 0.5 | 3.1415927 |
| 1 | 6.2831853 |
| 2 | 12.566371 |
| 3 | 18.849556 |
| 5 | 31.415927 |
| 10 | 62.831853 |
| 20 | 125.66371 |
| 25 | 157.07963 |
| 50 | 314.15927 |
| 100 | 628.31853 |
| 1,000 | 6283.1853 |
How to convert Turn to Radian
Multiply the turn value by 6.2831853 to get radians.
- Enter the number of turns you want to convert.
- The converter instantly shows the equivalent value in radians.
- Worked example: 15 turn × 6.2831853 = 94.24778 rad.
- Use the swap button to reverse the conversion (radian to turn).
About these units
Turn (turn)
- Definition
- A turn is one complete rotation, equal to 360 degrees or 2π radians.
- History
- The full turn is the most intuitive angle and underlies the definition of other units.
- Current use
- Turns describe rotations in engineering, mechanics, and everyday language.
Radian (rad)
- Definition
- A radian (rad) is the SI angle for which the arc length equals the radius; a full circle is 2π radians.
- History
- The concept was formalised in the 19th century and named in 1873.
- Current use
- Radians are the standard angle unit in mathematics and physics.
Frequently asked questions
How many radians are in a turn?
There are 6.2831853 rad in 1 turn. To convert, multiply the number of turns by 6.2831853.
How do I convert turns to radians?
Multiply the turn value by 6.2831853 to get radians. For example, 10 turn = 62.831853 rad.
Is this turn-to-radian converter free?
Yes. This converter is completely free, runs entirely in your browser, and requires no sign-up. Your inputs never leave your device.
Convert Turn to other angle units
| Unit | 1 Turn equals |
|---|---|
| Degree (°) | 360 ° |
| Radian (rad) | 6.2831853 rad |
| Gradian (grad) | 400 grad |
| Arcminute (') | 21600 ' |
| Arcsecond (") | 1296000 " |