Angular Velocity Calculator

Convert RPM, rad/s, deg/s and frequency. Compute angular displacement and revolutions completed.

Formulas

ω = 2π·f  (from frequency)
ω (rad/s) = RPM · 2π / 60
θ = ω · t  (angular displacement)
Revolutions = θ / (2π)

How to use

  1. Pick the unit of your angular velocity (RPM / rad/s / deg/s / Hz) and enter the value.
  2. Optionally enter a time to compute angular displacement and revolutions completed.
  3. Calculate.

Physics behind angular velocity

Angular velocity describes rotational motion the way linear velocity describes translation. The SI unit is radians per second. An engine turning at 3,000 RPM is rotating at 3,000·2π/60 ≈ 314 rad/s. Angular frequency ω is also the quantity that appears in simple harmonic motion (ω = 2π·f), making it central to oscillations and waves.

Worked example

3000 RPM for t = 2 s

ω = 3000·2π/60 ≈ 314.159 rad/s
f = 3000/60 = 50 Hz
θ = ω·t ≈ 628.32 rad
Revs = θ/(2π) = 100

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FAQs

What is angular velocity?

The rate of change of angular position, measured in rad/s.

How do I convert RPM to rad/s?

Multiply by 2π/60 ≈ 0.10472.