Radians to Revolutions Converter
Convert angle measurements from radians (rad) to revolutions (rev). One revolution equals 2π radians or 360 degrees.
radians (rad)
Result
0 rev
Common Radians to Revolutions Conversions
| Radians (rad) | Revolutions (rev) |
|---|---|
| π/6 (0.5236) rad | 1/12 rev (0.0833) |
| π/4 (0.7854) rad | 1/8 rev (0.125) |
| π/3 (1.0472) rad | 1/6 rev (0.1667) |
| π/2 (1.5708) rad | 1/4 rev (0.25) |
| π (3.14159) rad | 1/2 rev (0.5) |
| 3π/2 (4.7124) rad | 3/4 rev (0.75) |
| 2π (6.28319) rad | 1 rev |
| 4π (12.5664) rad | 2 rev |
How to Convert Radians to Revolutions
A revolution (also called a turn or cycle) is a complete 360° rotation. Since one revolution equals 2π radians, divide radians by 2π to get revolutions.
The Conversion Formula
revolutions = radians / (2π)
This can also be written as: revolutions = radians × 0.159155
Understanding the Conversion
The radian is defined such that a full circle contains exactly 2π radians. Therefore, to find how many complete revolutions an angle represents, simply divide by 2π.
Example: Converting 2π Radians to Revolutions
revolutions = 2π rad / (2π) = 6.28319 / 6.28319 = 1 revolution
This confirms that 2π radians equals exactly one complete revolution.
Applications of Revolutions
Revolutions are commonly used in:
- Rotational Speed: RPM (revolutions per minute) measures motor and engine speeds
- Astronomy: Orbital periods expressed as revolutions around a body
- Manufacturing: Lathe operations, drilling, and machining speeds
- Physics: Angular velocity and rotational dynamics
Related Units
Revolution is equivalent to:
- 1 turn (tr)
- 1 cycle
- 360 degrees
- 2π radians
- 400 gradians