Angular Velocity Calculator
Compute angular velocity (ω) in radians per second and RPM from a rotation period, a frequency, or a linear speed and radius.
Input source
Hz
Rotational rate in radians per second
- 1
Radians in one revolution
6.28319One full rotation sweeps 2π ≈ 6.2832 radians. - 2
Angular velocity ω
2π × 1 = 6.2832
How does this calculator work?
Angular velocity ω is rotation rate in radians per second. From a period use ω = 2π/T, from frequency ω = 2π·f, and from linear speed and radius ω = v/r. Convert to revolutions per minute with RPM = ω·60/2π, where f = ω/2π and T = 2π/ω.
Formula
How this is calculated
Angular velocity ω measures how fast something rotates, expressed in radians per second. Pick the input source that matches your data. If you know the period T (seconds for one full revolution), ω = 2π / T. If you know the rotational frequency f (revolutions per second, Hz), ω = 2π·f. If you know the linear (tangential) speed v of a point on the rim and the radius r from the axis, ω = v / r, because v = ω·r.
From ω the calculator derives the other common measures: RPM = ω·60 / 2π converts radians per second to revolutions per minute, frequency f = ω / 2π gives revolutions per second, and period T = 2π / ω gives the seconds per revolution. These four quantities all describe the same uniform rotation.
The model assumes constant (uniform) angular velocity and uses consistent SI units: seconds, hertz, metres, and metres per second. Inputs must be finite; a zero period or zero radius is undefined and returns no result. A zero frequency yields ω = 0 and an infinite period, which is reported as a non-finite value.
Frequently asked questions
Multiply the angular velocity in rad/s by 60 and divide by 2π. For example, 1 rad/s ≈ 9.549 RPM.
Frequency f counts full revolutions per second (Hz), while angular velocity ω counts radians per second. They are related by ω = 2π·f, since one revolution is 2π radians.
For a point at radius r from the axis, linear speed v = ω·r, so ω = v / r. A larger radius means a higher linear speed for the same angular velocity.
Also known as
TG we-Calculate Editorial Team. (2026). Angular Velocity Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/angular-velocity-calculator
TG we-Calculate Editorial Team. "Angular Velocity Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/angular-velocity-calculator.
TG we-Calculate Editorial Team, "Angular Velocity Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/angular-velocity-calculator
@misc{wecalculate_angular_velocity_calculator, title = {Angular Velocity Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/angular-velocity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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