# Angular Acceleration Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Oct 24, 2022

The angular acceleration calculator helps you find the angular acceleration of an object that rotates or moves around a circle. As you will soon see, the angular acceleration formula differs from the acceleration in linear motion, which you probably know very well.

Read on if you want to learn what are the angular acceleration units and what is the angular acceleration equation. You will find out that you can compute it with our angular acceleration calculator in two different ways.

You can also check our centrifugal force calculator, which is dedicated to circular motion too.

## Angular acceleration definition

The rotational movement of an object is usually described by a physical quantity called angular velocity. It measures the angle by which an object rotates in a specific time. For example, imagine that a carousel in an amusement park performs full rotation within ten seconds. Its angular velocity is one rotation (360°) per ten seconds or 36° per second. See our angular velocity calculator to learn more about angular velocity.

Let's assume that our carousel starts to rotate faster and faster, not 36° but 50°, then 64° per second. Angular acceleration describes this rate of change of angular velocity and is caused by torque.

In the next section, we will see how to find the rate of change of angular velocity, i.e., the angular acceleration.

💡 Not sure what torque is? Our torque calculator can help explain.

## Angular acceleration formula

Angular acceleration can be computed with our angular acceleration calculator in two different ways. We are using the below angular acceleration equations:

$\alpha = \frac{\omega_2 - \omega_1}{t},\quad \text{or:}\quad \alpha = \frac{a}{R},$

where:

• $\alpha$ – Angular acceleration;
• $\omega_1$ – Initial angular velocity;
• $\omega_1$ – Final angular velocity;
• $t$ – Time of change of angular velocity;
• $a$ – Tangential acceleration; and
• $R$ – Radius of the circle (or the distance from an axis of rotation).

Tangential acceleration acts as a linear acceleration, which is perpendicular to the radius of the circle.

🔎 When an angular velocity is a scalar (not a vector), we should call it angular speed or angular frequency. Check out our angular frequency calculator to learn more about it!

## Angular acceleration units

We can use several different units to express angular acceleration:

• The most common are units of angle per second squared (e.g., rad/s², °/s²). This unit nicely illustrates the meaning of angular acceleration since the linear acceleration is expressed in m/s² or ft/s².

• Sometimes, we omit the numerator leaving only the 1/s².

• Since angular velocity can be expressed in hertz Hz = 1/s, we can also use this in angular acceleration receiving Hz/s. We have used this convention in our angular acceleration calculator.

The conversion between the above angular acceleration units is as follows rad/s² = 1/s² = Hz/s.

Dominik Czernia, PhD
How would you like to calculate angular acceleration?
Method
Angular velocity difference
Angular velocity difference
Initial angular velocity
Final angular velocity
Time
sec
Angular acceleration
/s²
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