Angular Acceleration Calculator
This calculator finds angular acceleration from how fast a spin changes over time, using alpha = (omega_f - omega_i) / t. Enter the starting and ending angular velocity in rad/s and the elapsed time in seconds to get the result in rad/s^2. Supply a moment of inertia and it also returns the net torque, tau = I times alpha, in newton-metres.
How to use the angular acceleration calculator
- Enter the starting spin in the Initial omega field, in rad/s.
- Enter the ending spin in the Final omega field, in rad/s.
- Enter the elapsed Time in seconds, which must be greater than zero.
- Optionally enter a Moment of inertia in kg m^2 to also compute net torque.
- Read the angular acceleration and torque, then Copy the result if needed.
Examples
A wheel spinning up from rest
omega_i = 0, omega_f = 20 rad/s, t = 4 s, I = 0.5 kg m^2
alpha = 5 rad/s^2, torque = 2.5 N x m
A flywheel slowing to a stop
omega_i = 30, omega_f = 0 rad/s, t = 6 s
alpha = -5 rad/s^2 (torque blank, no inertia given)
A disc speeding up with inertia
omega_i = 10, omega_f = 25 rad/s, t = 3 s, I = 2 kg m^2
alpha = 5 rad/s^2, torque = 10 N x m
Frequently asked questions
What is the angular acceleration formula used here?
It is alpha = (omega_f - omega_i) / t, the final angular velocity minus the initial one, divided by the elapsed time. With both velocities in rad/s and time in seconds, the answer is in rad/s^2. The tool assumes the acceleration is constant over that interval.
How do I get torque from the angular acceleration?
Enter a moment of inertia in the last field. The tool then applies tau = I times alpha and shows the net torque in newton-metres. Leave the field blank and the torque cell simply stays empty.
What does a negative angular acceleration mean?
It means the object is slowing its rotation, because the final velocity is lower than the initial one. Going from 30 rad/s down to 0 over 6 seconds gives alpha = -5 rad/s^2. A negative moment of inertia is not allowed, so torque follows the sign of alpha.
Why must the time be greater than zero?
The formula divides by time, and dividing by zero is undefined. The tool requires a positive time and shows a message if the field is empty or zero, since a change that takes no time has no finite acceleration.
What units should I use?
Angular velocity is in radians per second, time in seconds, and angular acceleration comes out in radians per second squared. Moment of inertia is in kilogram metre squared, and torque is reported in newton-metres.
How do I convert RPM to rad/s before entering it?
Multiply revolutions per minute by 2 pi and divide by 60. For example 300 RPM is 300 times 6.2832 divided by 60, about 31.42 rad/s. Enter that converted value so the result stays in the correct units.
How precise is the result?
Values are rounded to nine decimal places to trim floating point noise while keeping fine detail. Whole-number inputs like the examples come out exact, and long decimals are cut off at the ninth place.
Can I use it for constant angular velocity?
If the initial and final velocities are equal, the acceleration is zero, and any moment of inertia gives zero torque. That is the correct physics for steady rotation with no net angular force.
Is anything I enter sent to a server?
No. The whole calculation runs locally in your browser, so the numbers you type are never uploaded, logged or stored anywhere.
Learn more
- Angular acceleration, torque and moment of inertia
How alpha, torque and moment of inertia connect through Newton's second law for rotation, with worked steps and unit conversions.
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