Turns to radians converter
Convert turns (rev) to radians (rad). Calculate a value, check the formula and compare common measurements.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Value | Enter value using the definition in the method and example. |
| From | Select the unit or currency in which the entered number is currently expressed. |
| To | Select the unit or currency you need for the answer. |
Understanding your result
The converted value describes the same angle quantity in the selected target unit. Display rounding does not add precision to the original measurement.
Common mistakes
- Confusing the source and target units, or overlooking a prefix or case-sensitive symbol.
- Entering radians when the value is in degrees.
Check your calculation
- Convert to the target unit and then reverse the direction. Within display rounding, you should recover the original value.
Read the angle measurement guide · Calculation checks, sources and review limits
How do I convert turns to radians?
Enter the value in turns to find the same angle quantity in radians. The number changes to match the unit; the underlying quantity stays the same. Check the definitions below when a unit has more than one convention.
Common uses
- Express an angle in degrees, radians or another supported unit.
- Translate angular measurements before a calculation.
How it works
For the displayed direction, 1 rev equals 6.28318530718 rad. The engine converts through the shared angle base quantity. Use consistent physical definitions; conversion changes the unit, not the measured quantity. The multiplier is derived from the two centralized unit factors. Keep full precision until the final result; displayed answers use up to 12 significant digits.
Worked example
10 rev converts to 62.8318530718 rad. For the reverse direction, swap the units and enter 62.8318530718 rad; the result is approximately 10 rev.
FAQ
How do I convert rev to rad?
rad = rev × 6.28318530718
Which definition is used?
The centralized unit definitions in our unit library are used.
Common values
Use “Swap units” above for the reverse conversion. Values below are rounded to six significant digits.
| turns | radians |
|---|---|
| 1 | 6.28319 |
| 5 | 31.4159 |
| 10 | 62.8319 |
| 20 | 125.664 |
| 30 | 188.496 |
| 50 | 314.159 |
| 100 | 628.319 |