Angular Velocity Calculator

ω = Δθ / Δt = 2π·f. Conversion between rad/s, rev/min, and Hz.

Inputs

Result

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General calculation reads

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How to use this calculator

  • Pick what you have.
  • Enter the value.
  • Read all units.

About this calculator

Angular velocity ω measures rotation rate. ω = 2πf where f is frequency in Hz. Common conversions: 60 RPM = 1 rev/s = 2π rad/s ≈ 6.28 rad/s. Earth's rotation: ω ≈ 7.27e-5 rad/s. Engine at 6000 RPM: ω ≈ 628 rad/s. Used in physics (rotational kinematics), engineering (motor specs), navigation (gyroscopes).

Frequently asked

rad/s vs. RPM?+
rad/s is SI / physics standard. RPM is engineering / consumer (motor labels). Convert: rad/s = RPM × 2π/60.
Why 2π?+
One full revolution = 2π radians. Defines the unit conversion.
Linear vs. angular?+
Linear v = ω × r (velocity at radius r). Linear at rim of 0.3m wheel at 60 RPM: v = 6.28 × 0.3 = 1.88 m/s.
Pendulum/oscillator ω?+
For SHM: ω = √(k/m). Different concept (angular frequency of oscillation, not actual rotation).
Engines and EVs?+
Gas engines: 6,000-8,000 RPM redline. EV motors: 12,000-18,000 RPM. F1: 18,000+ RPM.

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