Revolutions to Radians Converter
Convert angle measurements from revolutions (rev) to radians (rad). One revolution equals exactly 2π radians.
Common Revolutions to Radians Conversions
| Revolutions (rev) | Radians (rad) |
|---|---|
| 1/12 rev | π/6 (0.5236) rad |
| 1/8 rev | π/4 (0.7854) rad |
| 1/6 rev | π/3 (1.0472) rad |
| 1/4 rev | π/2 (1.5708) rad |
| 1/2 rev | π (3.14159) rad |
| 3/4 rev | 3π/2 (4.7124) rad |
| 1 rev | 2π (6.28319) rad |
| 2 rev | 4π (12.5664) rad |
| 10 rev | 20π (62.8319) rad |
How to Convert Revolutions to Radians
A revolution represents one complete rotation around a circle. Since the circumference of a unit circle is 2π, one revolution equals 2π radians.
The Conversion Formula
This can also be written as: radians = revolutions × 6.28318530718
Understanding the Conversion
The radian measure of an angle is defined as the ratio of arc length to radius. For a complete circle, the arc length equals the circumference (2πr), so the angle in radians is 2πr/r = 2π. This is why one revolution = 2π radians.
Example: Converting 1.5 Revolutions to Radians
radians = 1.5 rev × 2π = 1.5 × 6.28319 = 9.42478 rad (3π)
This represents one and a half complete rotations, or 540 degrees.
Angular Velocity Applications
Converting between revolutions and radians is essential for:
- RPM to rad/s: ω (rad/s) = RPM × 2π / 60
- Motor Calculations: Relating rotational speed to angular velocity
- Centripetal Force: F = mω²r requires ω in rad/s
- Wave Physics: Angular frequency ω = 2πf
Quick Reference
Common rotation angles:
- Quarter turn (90°) = 0.25 rev = π/2 rad
- Half turn (180°) = 0.5 rev = π rad
- Three-quarter turn (270°) = 0.75 rev = 3π/2 rad
- Full turn (360°) = 1 rev = 2π rad