Angular Acceleration Calculator
Find angular acceleration from change in speed.
Results update as you type.
How it works
Angular acceleration measures how quickly a rotating object's spin rate changes, and this calculator finds it from the change in angular velocity over time. You enter the initial angular velocity, the final angular velocity, and the time over which the change occurred, and it returns the angular acceleration in radians per second squared. The calculation mirrors linear acceleration exactly, just for rotation: it is the change in angular velocity divided by the elapsed time. Angular velocity, measured in radians per second, describes how fast something spins, and angular acceleration describes how fast that spinning speeds up or slows down. A positive result means the object is spinning faster over time, while a negative result means it is decelerating. This quantity is central to rotational dynamics, appearing whenever wheels spin up, motors start and stop, turntables change speed, or a figure skater alters their spin. It connects to torque through the rotational form of Newton's second law, where torque equals the moment of inertia times angular acceleration, the rotational counterpart of force equals mass times acceleration. Engineers designing rotating machinery, physicists analyzing motion, and students learning mechanics all use it. Make sure the angular velocities are in radians per second for a result in the standard units. Enter the initial and final angular velocities and the time to compute the angular acceleration.
α = (ω_final − ω_initial) / t
Angular acceleration is the rate of change of angular velocity, found by subtracting the initial angular velocity from the final and dividing by the time taken. It is measured in radians per second squared. A positive value means the rotation is speeding up, and a negative value means it is slowing down, the rotational analog of linear acceleration.
Source:Rotational dynamics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter initial angular velocity, final angular velocity and time.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Angular acceleration updates instantly as you type — no button to press.
Frequently asked questions
What is angular acceleration?
Angular acceleration is the rate at which an object's angular velocity changes over time, measured in radians per second squared. It is the rotational equivalent of linear acceleration. A positive value means the object is spinning faster, and a negative value means it is slowing down. It quantifies how quickly a rotation speeds up or slows.
How is angular acceleration calculated?
Subtract the initial angular velocity from the final angular velocity, then divide by the time over which the change happened. So going from 0 to 10 radians per second in 5 seconds gives an angular acceleration of 2 radians per second squared. The calculator does this from your three inputs.
How does it relate to torque?
Angular acceleration connects to torque through the rotational form of Newton's second law: torque equals the moment of inertia times angular acceleration. This mirrors force equals mass times acceleration for linear motion. So a larger torque, or a smaller moment of inertia, produces a greater angular acceleration for a rotating object.
What units should I use?
Enter the angular velocities in radians per second and the time in seconds to get angular acceleration in radians per second squared, the standard unit. If your values are in revolutions per minute or degrees per second, convert them to radians per second first, since mixing units will give an incorrect result.
What is the difference from linear acceleration?
Linear acceleration describes how fast an object's straight-line speed changes, while angular acceleration describes how fast its rotational speed changes. They are analogous: velocity corresponds to angular velocity, and acceleration to angular acceleration. A point on a rotating object experiences both, with its linear acceleration related to the angular acceleration times the radius.