By Zencalcy Editorial TeamLast reviewed About us
Angular velocity describes how fast something rotates, regardless of how large the rotating object is. It is the angle swept per unit time, usually quoted in radians per second, with revolutions per minute used for engines and motors.
Angular speed from angle turned and time taken.
ω = Δθ / Δt
ω is angular velocity in rad/s, Δθ is the angle swept in radians and Δt is the time in seconds. One full turn is 2π radians, so 1 rpm equals 2π/60 rad/s.
| Symbol | Meaning |
|---|---|
| ω | Angular velocity, in radians per second. |
| Δθ | Angle turned, in radians. |
| Δt | Time taken, in seconds. |
Ten full turns is 20π radians, so ω = 20π / 5 = 12.57 rad/s. That is 720° per second, or 120 rpm.
Continue with the Circular Motion Period Calculator, Angular Momentum Conservation Calculator, or the Moment of Inertia Calculator — or browse more rotational and periodic motion tools and all physics calculators.
The relationship between angular and linear motion, v = ωr, only works when the angle is in radians. Radians are the natural unit because arc length equals radius times angle.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026