Calculates how fast an object rotates through an angle over time.
How it works
The angle swept, in radians, is divided by the time taken to give angular velocity.
What this does not include
This does not include linear velocity — for straight-line speed, use this site’s velocity calculator instead, which handles distance over time rather than rotation.
How to use this calculator
- Enter the angle swept in radians and the time taken.
A worked example
An object rotates through 6.283185 radians (a full circle) in 2 seconds → 6.283185 ÷ 2 = 3.1416 rad/s.
An object rotates through 3.14159 radians (half a circle) in 1 second → also 3.1416 rad/s.
What the variables mean
| Variable | Meaning |
|---|---|
| Angle | Angular displacement, in radians |
| Time | Time taken to sweep through that angle |
Edge cases worth knowing
This calculator works in radians, not degrees. A full rotation is 2π (≈6.2832) radians, not 360 — a common source of mismatched results if degrees are entered directly.
Zero time makes the result undefined, the same way it does for linear velocity — no rotation can happen in zero time at a finite rate.
Frequently asked questions
Why is angular velocity measured in radians per second?
Radians are the natural unit for angle in physics calculations, since they relate directly to arc length and radius without needing extra conversion factors.
How does angular velocity relate to linear velocity?
For an object moving in a circle, linear velocity equals angular velocity multiplied by the radius of the circular path.
What’s a real-world example of angular velocity?
A spinning wheel, a rotating fan blade, or a planet’s rotation on its axis — anything completing rotation over time.
