# Angular Acceleration Calculator

URL: https://speedycalculator.com/calculators/physics/angular-acceleration/
Last updated: 2026-10-30

> The angular acceleration calculator finds how quickly a rotation speeds up or slows down – from the change in angular velocity over time, from the torque and moment of inertia, or from the tangential acceleration and radius.

## Inputs

- Method
- Initial angular velocity ω₀ (rad/s, rpm, Hz (rev/s), °/s)
- Final angular velocity ω₁ (rpm, rad/s, Hz (rev/s))
- Time t (s, ms, min, h, days)
- Torque τ (N·m, kN·m, lbf·ft, lbf·in, kgf·m)
- Moment of inertia I (kg·m², g·cm², lb·ft², lb·in²)
- Tangential acceleration a_t (m/s², ft/s², g, cm/s²)
- Radius r (m, cm, mm, km, in, ft, yd, mi)

## Results

- Angular acceleration α

## Formula

```
α = (ω₁ − ω₀)/t · α = τ/I · α = a_t / r
```

## Explanation

Angular acceleration is the rotational counterpart of linear acceleration. Spinning up a hard drive, a car wheel accelerating or a figure skater changing speed all involve angular acceleration, measured in rad/s².

### How to use the Angular Acceleration Calculator

- **Method**
- **Initial angular velocity ω₀**
- **Final angular velocity ω₁**
- **Time t**
- **Torque τ**
- **Moment of inertia I**
- **Tangential acceleration a_t**
- **Radius r**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the method. Angular velocities can be entered in rad/s, rpm or revolutions per second.

### Inputs explained

FieldWhat to enterMethodChoose one: Angular velocity difference, Torque and moment of inertia, Tangential acceleration and radiusInitial angular velocity ω₀Units: rad/s, rpm, Hz (rev/s), °/sFinal angular velocity ω₁Units: rpm, rad/s, Hz (rev/s)Time tUnits: s, ms, min, h, daysTorque τUnits: N·m, kN·m, lbf·ft, lbf·in, kgf·mMoment of inertia IUnits: kg·m², g·cm², lb·ft², lb·in²Tangential acceleration a_tUnits: m/s², ft/s², g, cm/s²Radius rUnits: m, cm, mm, km, in, ft …

## Worked example

Inputs — Method: Angular velocity difference; Initial angular velocity ω₀: 0 rad/s; Final angular velocity ω₁: 3,000 rpm; Time t: 5 s.

Results — **Angular acceleration α = 62.8319 rad/s²**.

## Key terms

- **Angular acceleration**: Rate of change of angular velocity.

## FAQ

**What is the unit of angular acceleration?**
Radians per second squared (rad/s²).

**How is it related to linear acceleration?**
a_t = α·r at radius r.

**What is the rotational version of F = ma?**
τ = I·α.

**Can angular acceleration be negative?**
Yes – when the rotation slows down.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)