# Rotational Kinetic Energy Calculator

URL: https://speedycalculator.com/calculators/physics/rotational-kinetic-energy/
Last updated: 2026-10-30

> The rotational kinetic energy calculator finds the energy of a spinning object from its moment of inertia and angular velocity.

## Inputs

- Angular velocity ω (rpm, rad/s, Hz (rev/s))
- Moment of inertia I (kg·m², g·cm², lb·ft², lb·in²)

## Results

- Rotational kinetic energy
- Angular momentum

## Formula

```
E = ½·I·ω²
```

## Explanation

A spinning object stores kinetic energy even if its centre does not move. Flywheels, turbines, wheels and planets all hold rotational kinetic energy; a rolling ball has both rotational and translational energy.

### How to use the Rotational Kinetic Energy Calculator

- **Angular velocity ω**
- **Moment of inertia I**

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

### How it works

Enter the moment of inertia and the angular velocity (rad/s, rpm or Hz).

### Inputs explained

FieldWhat to enterAngular velocity ωUnits: rpm, rad/s, Hz (rev/s)Moment of inertia IUnits: kg·m², g·cm², lb·ft², lb·in²

### What each result means

- **Rotational kinetic energy** = [Moment of inertia I]×[Angular velocity ω]^2÷2
- **Angular momentum** = [Moment of inertia I]×[Angular velocity ω]

### Example values

How the main result changes when **Angular velocity ω** changes and everything else stays at the example values above:

Angular velocity ω (rpm)Rotational kinetic energy (J)1,500616.85032,2501,387.91313,0002,467.40113,7503,855.31424,5005,551.65256,0009,869.6044

## Worked example

Inputs — Angular velocity ω: 3,000 rpm; Moment of inertia I: 0.05 kg·m².

Results — **Rotational kinetic energy = 2,467.4011 J**; Angular momentum = 15.70796 kg·m²/s.

## Key terms

- **Rotational kinetic energy**: ½Iω².

## FAQ

**How does speed affect rotational energy?**
It grows with ω² – double the rpm, four times the energy.

**What is the total energy of a rolling ball?**
½mv² + ½Iω².

**Where is rotational energy stored usefully?**
Flywheels and turbines.

**What are the units?**
Joules.


## 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)