How this calculator works
Angular velocity measures signed angle change per second. Angles can include full turns and are subtracted directly without wrapping. For a point moving on a circle, tangential velocity is angular velocity multiplied by radius. Angle-over-time modes give an average over the entered interval, rather than an instantaneous derivative.
Formula
omega = delta theta/t = (theta_f - theta_i)/t = v_t/r; rpm = 60 omega/(2 pi).
Worked example
An angle change of 12 rad in 3 s gives 4 rad/s. A point moving tangentially at 9 m/s on a 3 m radius circle has angular velocity 3 rad/s.
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Frequently asked questions
Should I subtract angles across zero degrees?
Use unwrapped angles that include complete turns. For example, motion from 350 to 370 degrees is a positive 20 degree change.
Can angular velocity be negative?
Yes. The sign specifies rotation opposite to your positive direction.
Does every point on a wheel have the same speed?
A rigid wheel has one angular velocity, while tangential speed increases with radius.