Angular Velocity Converter

Angular velocity is how fast something rotates, measured in SI as radians per second (rad/s). One full turn is 2π radians, and that factor is behind nearly every conversion on this page. Day to day, rotation is usually quoted in RPM (revolutions per minute), so swapping between RPM and rad/s is the most common reason to be here.

Key conversions:

• 1 rad/s = 57.296 degrees/s (180/π)
• 1 rad/s = 9.5493 RPM (60/2π)
• 1 rev/s = 6.2832 rad/s (2π)
• 1 RPM = 0.10472 rad/s (2π/60)

For scale:

• Earth’s rotation: 0.0000727 rad/s (one turn per 24 hours)
• A car engine at idle: about 700 RPM
• A hard drive: 5,400–7,200 RPM

Radians win in physics because they keep the math clean. Rotational energy, angular momentum, and the link to linear speed all assume rad/s. Degrees and RPM read more naturally to people, but each forces a conversion factor into the formula.

Don’t mix up angular velocity with the speed of a point on the rim. They’re tied together by radius: rim speed equals angular velocity times radius. Every point on a spinning disc shares one angular velocity, but the outer edge travels faster through space than the center. It’s the same reason the rim of a vinyl record covers more ground per turn than the label does.

A note on hertz, because it trips people up. Revolutions per second and hertz are the same thing numerically, so 1 rev/s is 1 Hz. Rad/s is often called angular frequency and written omega, and it is not the same number: omega equals 2π times the frequency in hertz. Read “50 Hz” as rad/s and you are out by a factor of 6.28, which is the single most common error in this corner of physics.