Convert Turns to Radians
1 turn is 6.28 rad. One turn is exactly 6.28318530718 radians.
One turn is 6.2831853 radians. To convert turns to radians, multiply by 6.2831853; to go the other way, divide by 6.2831853 or multiply by 0.15915494. 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. One full revolution — 360 degrees, 400 gradians, 2π radians.
Factor checked against the defining standard · How we check
- Turns × 6.2831853
1 * 6.28318536.283 rad
1 turn in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 6.283185307 rad | × 6.28318530718 |
| degrees | 360 ° | × 360 |
| gradians | 400 gon | × 400 |
| arcminutes | 21,600 ′ | × 21,600 |
| arcseconds | 1,296,000 ″ | × 1,296,000 |
| turns (as entered) | 1 turn | — |
| milliradians | 6,283.185307 mrad | × 6,283.18530718 |
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 turns to radians? The converter and the working
- 1.Take the measurement in turns.
- 2.Multiply by 6.2831853 — that is how many radians fit in one turn.
- 3.To go back the other way, divide by 6.2831853, or multiply by 0.15915494.
Worked example: 25 turns to radians
- Formula
- turn × 6.2831853 = rad
- Arithmetic
- 25 × 6.2831853 = 157.08 rad
- Answer
- 25 turn = 157.08 rad
The factor is rounded for display; the figure above is computed from the full value.
Turns to radians conversion table
| Turns | Radians |
|---|---|
| 1 turn | 6.28 rad |
| 2 turn | 12.57 rad |
| 3 turn | 18.85 rad |
| 4 turn | 25.13 rad |
| 5 turn | 31.42 rad |
| 6 turn | 37.7 rad |
| 7 turn | 43.98 rad |
| 8 turn | 50.27 rad |
| 9 turn | 56.55 rad |
| 10 turn | 62.83 rad |
| 12 turn | 75.4 rad |
| 15 turn | 94.25 rad |
| 20 turn | 125.66 rad |
| 25 turn | 157.08 rad |
| 50 turn | 314.16 rad |
| 100 turn | 628.32 rad |
| 200 turn | 1,256.64 rad |
| 300 turn | 1,884.96 rad |
| 500 turn | 3,141.59 rad |
| 1000 turn | 6,283.19 rad |
| 2000 turn | 12,566.37 rad |
| 5000 turn | 31,415.93 rad |
| 10000 turn | 62,831.85 rad |
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.
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.
How many radians are in a turn?
One turn is 6.2831853 radians. Going the other way, one radian is 0.15915494 turns. 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 turn.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Turns to radians. Rule Calculator. https://rulecalculators.com/convert/turn-to-radian
- MLA
- "Convert Turns to radians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/turn-to-radian.
- Chicago
- Rule Calculator. "Convert Turns to radians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/turn-to-radian.
The date is when the figures on this page were last checked against their source, not the day you opened it. Add your own access date if your style needs one.
Questions people actually ask
- How many radians are in a turn?
- 6.2831853. 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.
- How do I convert radians back to turns?
- Divide by 6.2831853, or multiply by 0.15915494 — they are the same operation.
Other angle conversions
Radians to turns — the same conversion the other way.