Revolutions to Radians (rev to rad) Converter
1 revolution equals 6.283185 radians — multiply the number of revolutions by 6.283185 (that is 2π) to convert. One full turn around a circle is exactly 2π radians, which is why a single revolution maps to roughly 6.28 rad.
The formula
To convert revolutions to radians, multiply by 2π:
radians = revolutions × 6.283185
For example, 10 rev × 6.283185 = 62.831853 rad. To reverse, divide by 6.283185 or multiply by 0.15915494.
Conversion table
| Revolutions (rev) | Radians (rad) |
|---|---|
| 1 | 6.283185 |
| 2 | 12.566371 |
| 3 | 18.849556 |
| 5 | 31.415927 |
| 10 | 62.831853 |
| 25 | 157.079633 |
| 50 | 314.159265 |
| 100 | 628.318531 |
| 250 | 1570.796327 |
| 500 | 3141.592654 |
| 1000 | 6283.185307 |
How to convert online
- Type the number of revolutions into the first box.
- Read the equivalent radians instantly in the second box.
- Or enter a radian value to convert back to revolutions — it works both ways.
Use the Revolution to Radian Converter — free and instant in your browser.
Where this conversion is used
Radians are the native angular unit in physics and programming trigonometry functions. Converting revolutions to radians is essential when a rotation counted in full turns must feed into equations for angular velocity, oscillation, or graphics code where sine and cosine expect radian inputs.
FAQ
How many radians are in a revolution?
One revolution equals 6.283185 radians, which is 2π. Multiply revolutions by 6.283185 — for example, 10 revolutions = 62.831853 radians.
What is the formula to convert revolutions to radians?
Radians = revolutions × 2π = revolutions × 6.283185. Half a revolution equals π, about 3.141593 radians.
How do I convert radians back to revolutions?
Divide by 6.283185, or multiply by 0.15915494. So 12.566371 radians = 2 revolutions.
Is the conversion exact?
The factor 6.283185 is 2π rounded to six decimals, so results are accurate for essentially all scientific and engineering work.
Related converters
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