Angular Velocity Calculator
Convert rpm to rad/s and calculate linear (tangential) speed at any radius instantly.
How it works
- 1Enter the rotational speed in rpm and the radius of the rotating point.
- 2The calculator applies ω = 2πN/60 to convert rpm to angular velocity in rad/s.
- 3Tangential (linear) speed is then computed as v = ω · r and shown in your chosen unit system.
Use cases
- Sizing motors and drives by matching shaft angular velocity to load requirements.
- Calculating belt or chain surface speed from sprocket radius and motor rpm.
- Determining the tip speed of fan blades, turbine rotors, or grinding wheels.
Frequently asked questions
What is the formula for angular velocity from rpm?
ω (rad/s) = 2π × N / 60, where N is the speed in revolutions per minute. For example, 1500 rpm gives ω = 2π × 1500 / 60 ≈ 157.08 rad/s.
How is tangential (linear) speed related to angular velocity?
v = ω · r, where r is the radius from the axis of rotation. At ω = 157.08 rad/s and r = 0.25 m, the surface speed is v ≈ 39.27 m/s.
What is the difference between angular velocity and frequency?
Frequency f (Hz) = N / 60 counts full revolutions per second. Angular velocity ω = 2πf scales frequency by 2π to give the rate of angle change in radians per second.
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