Angular Velocity Converter
Convert between rad/s, degrees/s, RPM, and revolutions per second instantly.
Type in any field and the others update automatically.
Type in any field — the others update instantly.
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.
How we build and check this converter
This converter runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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