Angular Velocity Calculator

Multiply RPM by 2 x pi and divide by 60, because one revolution is 2 x pi radians and one minute is 60 seconds. So 60 RPM equals 2 x pi, which the tool shows as 6.283185307 rad/s.

Multiply the angular velocity in rad/s by 180 and divide by pi, since a full circle is 2 x pi radians or 360 degrees. At 2 rad/s that gives 114.591559026 deg/s.

Yes. Switch the 'Input as' menu to rad/s and type your value. The tool then works backwards to RPM using rad/s times 60 divided by 2 x pi, and fills in deg/s and tangential speed as well.

Tangential speed is how fast a point on the rim travels along its circular path, in metres per second. It equals the angular velocity in rad/s times the radius, so without a radius the linear speed is undefined and the tool shows a dash.

Every point completes a rotation in the same time, but a point farther from the axis travels a longer circle in that time. Doubling the radius doubles the distance covered per turn, so tangential speed rises in direct proportion to the radius.

Values are rounded to nine decimal places, so conversions involving pi show many digits, such as 6.283185307 rad/s for 60 RPM. This keeps round-trip conversions accurate rather than truncating to a couple of digits.

The radius is in metres, so the tangential speed comes out in metres per second. For a radius given in centimetres or inches, convert it to metres first, for example divide centimetres by 100.

The tool requires values greater than zero for the speed and, when supplied, the radius. Zero or negative entries produce a short message asking for a positive number rather than a result.

No. Every conversion is computed in your browser with no network request, so the numbers you type are never uploaded or stored.