Convert Radians to Turns
1 radian is 0.16 turn. One radian is exactly 0.159154943092 turns.
One radian is 0.15915494 turns. To convert radians to turns, multiply by 0.15915494; to go the other way, divide by 0.15915494 or multiply by 6.2831853. The relation is exact but the figure is not: it is a rounding of a number that does not terminate, and it follows from NIST Special Publication 811. The angle subtending an arc equal to the radius.
Factor checked against the defining standard · How we check
- Radians × 0.15915494
1 * 0.15915490.159 turn
1 radian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians (as entered) | 1 rad | — |
| degrees | 57.29577951 ° | × 57.2957795131 |
| gradians | 63.66197724 gon | × 63.6619772368 |
| arcminutes | 3,437.746771 ′ | × 3,437.74677078 |
| arcseconds | 206,264.8062 ″ | × 206,264.806247 |
| turns | 0.1591549431 turn | × 0.159154943092 |
| milliradians | 1,000 mrad | × 1,000 |
Factors are entered by hand from NIST Special Publication 811 rather than derived from a units library, so the ones that terminate are exact rather than rounded.
How do you convert radians to turns? The converter and the working
- 1.Take the measurement in radians.
- 2.Multiply by 0.15915494 — that is how many turns fit in one radian.
- 3.To go back the other way, divide by 0.15915494, or multiply by 6.2831853.
Worked example: 25 radians to turns
- Formula
- rad × 0.15915494 = turn
- Arithmetic
- 25 × 0.15915494 = 3.98 turn
- Answer
- 25 rad = 3.98 turn
The factor is rounded for display; the figure above is computed from the full value.
Radians to turns conversion table
| Radians | Turns |
|---|---|
| 1 rad | 0.16 turn |
| 2 rad | 0.32 turn |
| 3 rad | 0.48 turn |
| 4 rad | 0.64 turn |
| 5 rad | 0.8 turn |
| 6 rad | 0.95 turn |
| 7 rad | 1.11 turn |
| 8 rad | 1.27 turn |
| 9 rad | 1.43 turn |
| 10 rad | 1.59 turn |
| 12 rad | 1.91 turn |
| 15 rad | 2.39 turn |
| 20 rad | 3.18 turn |
| 25 rad | 3.98 turn |
| 50 rad | 7.96 turn |
| 100 rad | 15.92 turn |
| 200 rad | 31.83 turn |
| 300 rad | 47.75 turn |
| 500 rad | 79.58 turn |
| 1000 rad | 159.15 turn |
| 2000 rad | 318.31 turn |
| 5000 rad | 795.77 turn |
| 10000 rad | 1,591.55 turn |
What is a radian?
The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
What is a turn?
One full revolution — 360 degrees, 400 gradians, 2π radians. Gear ratios, threads per turn and rotational counts are all stated in these.
How many turns are in a radian?
One radian is 0.15915494 turns. Going the other way, one turn is 6.2831853 radians. Both figures come from the same defined relation rather than from a measurement, which is why they are the same today as they were in 1959.
Every angle unit here
The whole group — 7 units with their symbols and the size of each one in radians — is on the conversion index, along with every pair it makes. The table above already gives each of them relative to a radian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Radians to turns. Rule Calculator. https://rulecalculators.com/convert/radian-to-turn
- MLA
- "Convert Radians to turns." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/radian-to-turn.
- Chicago
- Rule Calculator. "Convert Radians to turns." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/radian-to-turn.
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Questions people actually ask
- How many turns are in a radian?
- 0.15915494. One full revolution — 360 degrees, 400 gradians, 2π radians. Gear ratios, threads per turn and rotational counts are all stated in these.
- How do I convert turns back to radians?
- Divide by 0.15915494, or multiply by 6.2831853 — they are the same operation.
Other angle conversions
Turns to radians — the same conversion the other way.