Angular Acceleration Calculator
α from change in angular velocity over time.
Enter your values
Enter the initial angular velocity in rad/s.
Enter the final angular velocity in rad/s.
Enter the time in s.
Enter the radius in m.
Enter the moment of inertia in kg·m².
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Angular acceleration
- 6.28 rad/s²
- Tangential acceleration
- 1.884 m/s²
- Torque required
- 12.56 N·m
- Angle turned
- 78.5 rad
- Revolutions
- 12.494
Quick answer
Angular acceleration is α = (ω₂ − ω₁) ÷ t, the rate at which angular velocity changes, measured in radians per second squared.
α = Δω ÷ t
At a glance
| What it does | α from change in angular velocity over time. |
|---|---|
| Category | Physics |
| Inputs needed | Initial angular velocity, Final angular velocity, Time, Radius, Moment of inertia |
| Main output | Angular acceleration |
| Formula | α = Δω ÷ t |
| Cost | Free — no sign-up, no download |
How to use the Angular Acceleration Calculator
- 1Enter the starting and finishing angular velocity.
- 2Enter the time over which the change happened.
- 3Add radius and inertia for tangential acceleration and torque.
Inputs explained
- Initial angular velocity(rad/s)
- Enter the initial angular velocity in rad/s.
- Final angular velocity(rad/s)
- Enter the final angular velocity in rad/s.
- Time(s)
- Enter the time in s.
- Radius(m)
- Enter the radius in m.
- Moment of inertia(kg·m²)
- Enter the moment of inertia in kg·m².
Worked example
Using the values the calculator loads with:
Inputs
- Initial angular velocity0 rad/s
- Final angular velocity31.4 rad/s
- Time5 s
- Radius0.3 m
- Moment of inertia2 kg·m²
Results
- Angular acceleration6.28 rad/s²
- Tangential acceleration1.884 m/s²
- Torque required12.56 N·m
- Angle turned78.5 rad
- Revolutions12.494
Frequently asked questions
How do you convert RPM to rad/s?
Multiply RPM by 2π and divide by 60 — 300 RPM is 31.4 rad/s.
Is angular acceleration the same as tangential?
No — tangential acceleration is α × r and is measured in m/s² along the rim.
What do I need to enter into the Angular Acceleration Calculator?
Just 5 values: initial angular velocity, final angular velocity, time, radius, moment of inertia. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Angular Acceleration Calculator work out the answer?
Angular acceleration is α = (ω₂ − ω₁) ÷ t, the rate at which angular velocity changes, measured in radians per second squared. It applies the formula α = Δω ÷ t and shows the working so you can check each step by hand.
Is the Angular Acceleration Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.