Angular Velocity from RPM Calculator
Convert revolutions per minute into angular velocity in rad/s, and find the linear speed at a given radius.
How it works
ω = 2π · rpm ÷ 60 · v = ω · r
One revolution sweeps 2π radians, and rpm counts revolutions per minute, so multiplying by 2π and dividing by 60 gives radians per second. Angular velocity ω describes how fast the whole body turns regardless of size, while the linear (tangential) speed v = ωr grows with distance from the axis — the rim of a wheel moves faster than a point near the hub.
Worked example
At 3,000 rpm, ω = 2π × 3,000 ÷ 60 = 314.16 rad/s. A point 0.15 m from the axis has a linear speed of 314.16 × 0.15 = 47.12 m/s.
Sources: Angular velocity — Wikipedia
Frequently asked questions
How do I convert rpm to rad/s?
Multiply rpm by 2π and divide by 60. Each revolution is 2π radians, and there are 60 seconds in a minute, so 60 rpm equals about 6.283 rad/s.
What is the difference between angular and linear speed?
Angular speed (rad/s) is the same for every point on a rigid rotating body. Linear speed (m/s) depends on the radius — v = ωr — so points farther from the axis travel faster.
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This calculator is for educational purposes. Double-check important results before acting on them.