Angular Velocity Calculator
This angular velocity calculator finds angular velocity in two ways. You can either use the angle change in the period of time or apply the linear velocity and a given radius.
The formula
ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ
The same equations, different letters
Every equation of rotational kinematics is its linear counterpart with angle replacing displacement, angular velocity replacing velocity, and angular acceleration replacing acceleration. The correspondence is exact, because both describe motion whose second derivative is constant — which is why this page uses the same solver as the linear one.
Work in radians, not degrees. A radian is defined so that arc length is simply rθ, which makes every conversion between linear and angular quantities a plain multiplication by the radius: v = ωr, a = αr. In degrees each of those would need a factor of π/180, and that factor is the single commonest source of error in rotational problems.
Note that revolutions per minute is not an angular velocity in SI terms — multiply by 2π/60 to get rad/s. The conversion is shown above both ways.