Rotational Kinetic Energy Calculator

Calculate the energy stored in a spinning body from its moment of inertia and angular speed.

About Rotational Kinetic Energy Calculator

Rotational energy mirrors the linear form with moment of inertia in place of mass and angular velocity in place of speed. Because it scales with ω², flywheel energy is dominated by speed rather than mass. Flywheel storage runs at very high rpm precisely because energy scales with the square of speed but only linearly with inertia.

Formula

Rotational Kinetic Energy

E = ½ I ω²

I: Moment of inertia in kilogram metres squared
ω: Angular velocity in radians per second

Worked example

With the default values below, Rotational Kinetic Energy Calculator returns Rotational Kinetic Energy of 123,245.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Moment of inertiaminimum 0 kg m2: 2.5 kg m2
Angular velocityminimum 0 rad/s: 314 rad/s

Results

Rotational Kinetic Energy: 123,245.00 J
Rotational Kinetic Energy: 123.245 kJ
Rotational Speed: 2,998.5 rpm
Energy Stored: 34.2347 Wh
Energy at Double Speed: 492,980.00 J

Step by step

1Values used
2Rotational Kinetic Energy
3Rotational Kinetic Energy= 123,245.00 J
4Rotational Kinetic Energy= 123.245 kJ
5Rotational Speed= 2,998.5 rpm
6Energy Stored= 34.2347 Wh
7Energy at Double Speed= 492,980.00 J

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Rotational Kinetic Energy calculated?

E = ½ I ω² Rotational energy mirrors the linear form with moment of inertia in place of mass and angular velocity in place of speed. Because it scales with ω², flywheel energy is dominated by speed rather than mass.

Why does Rotational Kinetic Energy matter?

Flywheel storage runs at very high rpm precisely because energy scales with the square of speed but only linearly with inertia.

What values do I need to enter?

This calculator takes 2 inputs: Moment of inertia, Angular velocity. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.