Angular Velocity Calculator
RPM, rad/s, degrees and period, all at once.
Work out Angular Velocity. RPM, rad/s, degrees and period, all at once. Free, with no account and nothing to download.
Optional — gives the speed at that distance from the axis.
Angular velocity
6.2832 rad/s
60 rpm · one turn every 1 s
Angular velocity is the same everywhere on a rotating body — every point on a spinning wheel completes a turn in the same time. Linear speed is not: it grows with distance from the axis, which is why the rim of a wheel travels much further per revolution than the hub. That difference is the whole principle behind gears, centrifuges and why the tip of a helicopter blade can approach the speed of sound while the rotor head barely moves. Radians per second is the unit the physics is written in; rpm is the unit machinery is specified in. The factor between them is 2π/60, which is where a stray 9.55 in someone's working usually comes from.
How the Angular Velocity Calculator works
Enter a rotation rate in whichever unit you have it and get all the others, plus the linear speed at any radius. RPM is how machinery is specified and rad/s is how the physics is written, and the conversion between them is where a stray factor usually creeps in.
Also known as: rpm to rad/s converter · rotational speed calculator · angular frequency calculator · rpm to m/s calculator
Frequently asked questions
How do I convert RPM to rad/s?
Multiply by 2π and divide by 60, which is about 0.1047. So 60 rpm is 6.283 rad/s — one full turn per second.
What is the difference between angular and linear velocity?
Angular velocity is the same everywhere on a rotating body; linear velocity grows with distance from the axis. The rim of a wheel travels much further per turn than the hub, at the same rpm.
How do I find speed at the rim?
v = ωr, using angular velocity in radians per second. A 2 m radius at 60 rpm gives 12.6 m/s at the rim.
Why do radians rather than degrees?
Because v = ωr only works in radians. The radian is defined so that arc length equals angle times radius, which makes every rotational formula drop its conversion factors.
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