# Rotational Kinetic Energy Calculator

Created by Dominik Czernia, PhD candidate
Last updated: Jul 01, 2022

With our rotational kinetic energy calculator, you can use the rotational energy formula without going into the tedious process of computation or unit change. To estimate the energy, you need to provide two physical quantities:

1. Angular velocity - check out our other calculator to learn how to find angular velocity.
2. Moment of inertia - the equivalent of the mass for kinetic energy. You can compute this value using the mass moment of inertia calculator.
3. The calculator will show the result automatically after receiving the inputs. You don't need to know how to calculate rotational kinetic energy at all!

The article below explains the rotational kinetic energy formula and how to find the rotational kinetic energy for a rotating ball as an example.

## Rotational kinetic energy formula

The equation for rotational kinetic energy is the following:

$E = \frac{1}{2} \times I \times \omega^2$

where:

• $E$ - The rotational kinetic energy, usually expressed in joules;
• $I$ - The moment of inertia, expressed in $\text{kg}\cdot\text{m}^2$; and
• $\omega$ - The angular velocity in radians per second.

That's basically it! You now know how to find rotational kinetic energy by hand. Check the torque calculator to learn about another physical quantity related to rotational motion, or read about its units and how to convert convert Nm to ft lbs and vice-versa.

## Rotational kinetic energy calculator - an practical example

Let's solve the rotational energy formula for the case of a rotating ball with the rotational kinetic energy calculator:

1. Enter the angular velocity of the ball. We assume it's rotating with $60 \text{ revolutions per minute (RPM)}$ or $6.283 \text{ rad/s}$. You can use the unit switcher in our tool if you want to use other units.
2. Find the ball's moment of inertia using the equation $I = \frac{2}{5}\times m \times r^2$, where $m$ is the mass and $r$ the radius of the ball. In our case, we estimated it as $I = 1.25\text{ kg}\cdot\text{m}^2$.
3. The calculator will automatically use the equation for rotational kinetic energy and present the result of $24.674 \text{ J}$.

Good job! You just solved the problem of how to calculate rotational kinetic energy.

Dominik Czernia, PhD candidate
Angular velocity
Moment of inertia
lb*ft²
Rotational kinetic energy
J
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