Angular Velocity Calculator

What the Angular Velocity Calculator does

Spin a wheel and every point on it sweeps through angle as time passes, and that rate is angular velocity. The calculator offers two routes: Angular Velocity (via Time to Turn Angle), or Angular Velocity (via Linear Velocity) from Linear Velocity and Path Radius.

Motor and gear designers use it daily because datasheets list rpm while physics uses rad/s. Students and machine builders use the tool to shuttle between the two scales without slipping a decimal. Fans, turbines, hard drives and merry-go-rounds all follow the same rules, so one tool serves classroom labs and factory floors alike.

Two formulas for one quantity

The time method uses omega = theta/t: turn through 12 radians in 4 seconds and omega equals 3 rad/s. The linear method uses omega = v/r, so a wheel edge moving 20 m/s on a 0.5 m Path Radius spins at 40 rad/s.

Conversion takes one step: rad/s times 9.5493 gives rpm, since one revolution covers 2 pi radians. Our 3 rad/s wheel therefore turns at about 28.6 rpm, while a drill spinning 3000 rpm runs near 314 rad/s.

How to use the calculator

Pick a mode, then in the angle version enter Angle turned in radians and Time taken in seconds. In the linear version enter Linear Velocity in meters per second and Path Radius in meters, measured from the center to the moving point. Angles given in degrees should be converted, since 360 degrees equals about 6.283 radians.

Press Calculate and read Angular Velocity in rad/s, multiplying by 9.5493 for rpm if needed. Pitfall: always use radius, never diameter; typing a 1 m diameter into the radius box doubles your true rotational speed.