Angular Acceleration Calculator

Formula

How this is calculated

Angular acceleration α is the rate at which angular velocity changes with time, measured in radians per second squared (rad/s²). It is the rotational analogue of linear acceleration. Three equivalent routes give the same α depending on what you know.

If you know the initial and final angular velocities and the time interval, use α = (ω_f − ω_i) / t — the kinematic definition. This assumes constant angular acceleration over the interval. If you know the net torque τ (N·m) acting on a body and its moment of inertia I (kg·m²), use Newton's second law for rotation: α = τ / I. Moment of inertia depends on mass distribution — a solid disk of mass m and radius r has I = ½mr², while a point mass at radius r has I = mr². If you know the tangential linear acceleration aₜ of a point on the rim and its distance r from the rotation axis, use α = aₜ / r, since tangential and angular acceleration are linked by aₜ = α·r.

The calculator converts rad/s² to degrees/s² (×180/π) and to RPM/s (×60/2π) for convenience. The model assumes rigid-body rotation about a fixed axis with constant α. Non-rigid bodies and precessing axes require more advanced treatment.