Turns to Radians
Type a value in Turns and get the result in Radians, calculated exactly.
90 Turns ≈ 565.4866776 Radians
Conventional factorRounded for display to about 10 significant digits.
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Range -50 – 100 tr = -314.159 – 628.319 rad
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Formula
rad = tr × 6.28318530718
To convert Turns to Radians, multiply the value by 6.28318530718.
Worked examples
- 0 tr × 6.28318530718 = 0 rad
- 90 tr × 6.28318530718 ≈ 565.4866776 rad
- 100 tr × 6.28318530718 ≈ 628.3185307 rad
This factor rests on a conventional or rounded value.
Conversion table
| Turns (tr) | Radians (rad) |
|---|---|
| 1 | ≈ 6.283185 |
| 5 | ≈ 31.41593 |
| 10 | ≈ 62.83185 |
| 15 | ≈ 94.24778 |
| 30 | ≈ 188.4956 |
| 45 | ≈ 282.7433 |
| 60 | ≈ 376.9911 |
| 90 | ≈ 565.4867 |
| 120 | ≈ 753.9822 |
| 135 | ≈ 848.23 |
| 180 | ≈ 1,130.973 |
| 270 | ≈ 1,696.46 |
| 360 | ≈ 2,261.947 |
Values marked ≈ are rounded; the rest are exact.
Reverse table: Radians to Turns
| Radians (rad) | Turns (tr) |
|---|---|
| 1 | ≈ 0.1591549 |
| 5 | ≈ 0.7957747 |
| 10 | ≈ 1.591549 |
| 15 | ≈ 2.387324 |
| 30 | ≈ 4.774648 |
| 45 | ≈ 7.161972 |
| 60 | ≈ 9.549297 |
| 90 | ≈ 14.32394 |
| 120 | ≈ 19.09859 |
| 135 | ≈ 21.48592 |
| 180 | ≈ 28.64789 |
| 270 | ≈ 42.97183 |
| 360 | ≈ 57.29578 |
Unit definitions
- Turns tr
- One full revolution: exactly 360 degrees.
- Radians rad
- The SI unit of angle: 180/π degrees, about 57.29578°.
Questions people ask
Turns to Radians: what is the conversion factor?
One tr is ≈ 6.283185307 rad.
How do I convert Turns to Radians?
Use the formula above. For example, 90 tr = ≈ 565.4866776 rad.
Is the conversion exact?
Very nearly. One of the units is based on a conventional or rounded value, so treat the result as a close approximation.
Factors checked 19 October 2026.