Angular Frequency Calculator

Use the angular frequency calculator to find the angular frequency (also known as angular velocity) of all rotating and oscillating objects.

Clear
Frequency at the final speed5 Hz
Angular displacement31.415927 radsolved from the three you gave
Angular acceleration15.707963 rad/s²
Initial angular velocity (given)0 rad/s
Final angular velocity (given)31.415927 rad/s
Time (given)2 s
Angular displacement in degrees1,800°
Revolutions turned5
Final speed in rpm300 rpm
Average angular velocity15.707963 rad/s

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.