Angular Acceleration Calculator
Enter an initial and final angular velocity and the time between them to get the angular acceleration in rad/s² — and see whether the rotation is speeding up or slowing down.
Speeding up or slowing down
Enter the two angular velocities and the time and the calculator returns the angular acceleration (α = (ω₂ − ω₁) / t) in rad/s².
Use SI units
Angular velocities in radians per second and time in seconds give the answer in rad/s² — convert rpm with × 2π ÷ 60 before you start.
What is an angular acceleration calculator?
The rate of change of spin
An angular acceleration calculator turns three measurements — a starting angular velocity, a finishing angular velocity, and the time between them — into the angular acceleration: how quickly a spinning object's rotation rate is changing. Angular acceleration is the rotational counterpart of ordinary acceleration, measured in radians per second squared (rad/s²). A positive value means the spin is getting faster, while a negative value means it is slowing down. It is the number behind a flywheel running up to speed, a wheel braking to a stop, and the torque a motor must supply to change a rotor's speed.
Enter an initial and final angular velocity in rad/s and the time in seconds to get the angular acceleration in rad/s² instantly.
Angular acceleration is the change in angular velocity divided by the time over which the change happens.
α = (ω₂ − ω₁) / tSubtract the initial angular velocity ω₁ from the final angular velocity ω₂, then divide by the elapsed time t. Suppose a rotor starts at rest (0 rad/s) and reaches 20 rad/s after 4 seconds: the change is 20 − 0 = 20 rad/s, and dividing by 4 seconds gives an angular acceleration of 5 rad/s². Because the velocities can be zero or negative, the result can come out positive (speeding up) or negative (slowing down); only the time must be greater than zero.
The formula is exact, but a couple of practical points are worth keeping in mind.
Average value over the interval and consistent units
This calculator gives the average angular acceleration over the interval, not the instantaneous value at a single moment — if the rate of change varies, the true acceleration may be higher or lower at points within the interval. Keep your units consistent: radians per second for the angular velocities and seconds for the time, or the rad/s² will be wrong. Convert revolutions per minute to rad/s by multiplying by 2π and dividing by 60 before you enter the values.