Radians to Revolutions (rad to rev) Converter
1 radian equals 0.15915494 revolutions — multiply the number of radians by 0.15915494 (or divide by 2π) to convert. Because one full revolution is 2π radians (about 6.283185 rad), a single radian is only a small fraction of a turn, which is why the factor is well under 1.
The formula
To convert radians to revolutions, multiply by the exact factor:
revolutions = radians × 0.15915494
For example, 10 rad × 0.15915494 = 1.591549 rev. To reverse the calculation, divide by 0.15915494 or multiply by 6.283185.
Conversion table
| Radians (rad) | Revolutions (rev) |
|---|---|
| 1 | 0.15915494 |
| 2 | 0.31830989 |
| 3 | 0.47746483 |
| 5 | 0.79577472 |
| 10 | 1.59154943 |
| 25 | 3.97887358 |
| 50 | 7.95774715 |
| 100 | 15.91549431 |
| 250 | 39.78873577 |
| 500 | 79.57747155 |
| 1000 | 159.15494309 |
How to convert online
- Type the number of radians into the first box.
- Read the equivalent revolutions instantly in the second box.
- Or enter a revolution value to convert back to radians — it works both ways.
Use the Radian to Revolution Converter — free and instant in your browser.
Where this conversion is used
Radians-to-revolutions conversion shows up in rotational mechanics, motor and gear design, robotics, and computer graphics, where angular position is often stored in radians but reported to people as full turns. Expressing a shaft's rotation as revolutions is far more intuitive than a long radian value when you are counting how many times something has spun.
FAQ
How many revolutions are in a radian?
One radian equals 0.15915494 revolutions. Multiply radians by 0.15915494 to convert — for example, 10 radians = 1.591549 revolutions.
What is the formula to convert radians to revolutions?
Revolutions = radians × 0.15915494. This equals dividing by 2π, since one revolution is exactly 2π radians.
How do I convert revolutions back to radians?
Divide by 0.15915494, or multiply by 6.283185. So 1 revolution = 6.283185 radians.
Is the conversion exact?
The factor 0.15915494 is 1/(2π) rounded to eight decimals, so results are accurate for virtually all engineering and math work.
Related converters
Built by ByteVancer
ByteTools is a free product of ByteVancer, a software and web development studio. If you need custom web apps, calculators, or engineering tooling built for your team, ByteVancer can help — explore our services and get in touch.
Recommended reading
Revolutions to Radians (rev to rad) Converter
1 revolution equals 6.283185 radians (2π). Use the exact factor, formula, and reference table to convert revolutions to radians fast.
Revolutions to Gradians (rev to grad) Converter
1 revolution equals 400 gradians. Use the exact factor, formula, and reference table to convert revolutions to gradians instantly.
Revolutions to Degrees (rev to °) Converter
1 revolution equals 360 degrees. Use the exact factor, formula, and reference table to convert revolutions to degrees instantly.
Radian to Gradian Converter (rad to grad)
1 radian equals 63.661977 gradians. Convert radians to gradians instantly with the exact factor, formula and a reference table.