Mechanical

Flywheel Energy Calculator

Calculate flywheel stored energy, usable energy between speeds, moment of inertia, angular velocity, rim speed, and Wh equivalent.

Formula E = 1/2 I omega^2Reviewed Sep 1, 2026

A flywheel stores energy as rotational kinetic energy: E = 1/2 I omega^2. This calculator estimates energy from mass, radius, RPM, and a selected inertia model, then adds the practical checks users usually need next: moment of inertia, angular speed, rim speed, energy per mass, watt-hour equivalent, and the usable energy released when the flywheel slows from one RPM to another.

Calculation Bench

Solve for

Inertia Model

01Flywheel Mass

m · total rotating mass for this inertia model

02Outer Radius

R · outer radius, not diameter

03Rotational Speed

n1 · operating speed before conversion to rad/s

Use radius, not diameter. If your CAD model gives mass moment of inertia directly, choose Custom I.

Solution

Enter flywheel geometry and RPM to calculate stored rotational energy.

E = 1/2 Iω²

Formula Sheet

E=\dfrac{1}{2}I\omega^2

\Delta E=\dfrac{1}{2}I(\omega_1^2-\omega_2^2)

\omega=\dfrac{2\pi n}{60}

I=\dfrac{1}{2}mR^2

I=\dfrac{1}{2}m(R_o^2+R_i^2)

I=mR^2

v=\omega R

EStored Energy
Delta EUsable Energy
IMoment of Inertia
mMass
ROuter Radius
RoOuter Ring Radius
RiInner Ring Radius
nRotational Speed
omegaAngular Speed
vRim Speed

Flywheel Inertia Model Guide

Model	Moment of inertia	Use when
Solid disk	I = 1/2 mR²	Mass is spread through a uniform circular disk
Thick ring	I = 1/2 m(Ro² + Ri²)	Flywheel has a bore or annular rim section
Thin rim	I = mR²	Most mass is concentrated near the outer radius
Custom I	I entered directly	CAD, test data, or a datasheet gives kg·m²

Variables & Units

Symbol	Variable	Description	Common Units
E	Stored Energy	Rotational kinetic energy at the entered speed.	J, kJ, Wh, ft·lbf
Delta E	Usable Energy	Energy released between the initial and final speeds.	J, kJ, Wh
I	Moment of Inertia	Mass moment of inertia about the spin axis, in kg·m².
m	Mass	Total rotating mass represented by the selected inertia model.	kg, lb
R	Outer Radius	Outer radius used for solid disk or thin-rim inertia and rim speed.	mm, m, in
Ro	Outer Ring Radius	Outer radius for thick-ring inertia.	mm, m, in
Ri	Inner Ring Radius	Bore or inner radius for thick-ring inertia.	mm, m, in
n	Rotational Speed	Flywheel speed before conversion to rad/s.	rpm, rad/s
omega	Angular Speed	Rotational speed in radians per second.
v	Rim Speed	Outer surface speed, useful as a quick stress-screening signal.	m/s, ft/min

How to Use This Calculator

01Choose Stored Energy when you want total energy at one operating speed.
02Choose Usable Speed Drop when you want the energy released between an initial RPM and a lower final RPM.
03Pick the inertia model that best matches the mass distribution: solid disk, thick ring, thin rim, or custom moment of inertia.
04Enter mass and outer radius for geometry-based models; thick-ring mode also needs inner radius.
05Read energy in kJ and Wh, then check rim speed. High rim speed is often the first warning that stress, containment, balancing, and bearing design need specialist review.

How the Formula Works

RPM is converted to angular speed with omega = 2 pi n / 60 before the energy equation is applied.

For a solid disk, I = 1/2 mR^2. For a thick ring, I = 1/2 m(Ro^2 + Ri^2). For a thin rim, I = mR^2. A rim-heavy flywheel stores more energy than a solid disk of the same mass and outer radius.

Stored energy scales with speed squared. Doubling RPM quadruples energy if the moment of inertia stays the same.

In speed-drop mode, usable energy is the difference between the high-speed and low-speed stored energies: Delta E = 1/2 I(omega1^2 - omega2^2).

Rim speed is v = omega R. It is not a full stress calculation, but it is a useful sanity-check output because flywheel stress also rises strongly with speed.

Worked Example 01

10 kg solid disk at 3000 rpm

Known

Mass: 10 kg
Outer radius: 0.2 m
Speed: 3000 rpm

Formula

E = 1/2 I omega^2

Substitution

I = 1/2 x 10 x 0.2^2 = 0.2 kg·m²; omega = 2pi x 3000 / 60 = 314.16 rad/s; E = 1/2 x 0.2 x 314.16^2

Result

E ≈ 9.87 kJ, or about 2.74 Wh

This matches the standard solid-disk example. The rim speed is about 62.8 m/s, so stress and containment should be reviewed before treating this as a safe hardware design.

Worked Example 02

Usable energy from 3000 rpm down to 2500 rpm

Known

Mass: 50 kg
Outer radius: 0.3 m
Initial speed: 3000 rpm
Final speed: 2500 rpm

Formula

Delta E = 1/2 I (omega1^2 - omega2^2)

Substitution

I = 1/2 x 50 x 0.3^2 = 2.25 kg·m²; Delta E = 1/2 x 2.25 x (314.16^2 - 261.80^2)

Result

Delta E ≈ 33.9 kJ, or about 9.42 Wh

The flywheel still contains energy at 2500 rpm. Only the difference between the two stored-energy levels is usable over that allowed speed drop.

Applications

01Estimating stored energy in an engine, press, generator, or test rig flywheel
02Comparing solid disk, thick ring, and rim-heavy flywheel concepts
03Estimating usable energy when speed is allowed to droop between two RPM limits
04Converting flywheel energy to Wh for comparison with electrical storage
05Screening rim speed before moving to stress and burst-speed analysis

Assumptions

01The flywheel is a rigid body spinning about its central axis.
02Mass distribution is approximated by the selected inertia model.
03Speed is steady for stored-energy mode; speed-drop mode uses the difference between two steady speeds.
04Rim speed is a screening signal only, not a substitute for a rotating-disk stress or burst-speed calculation.

Where This Model Stops

01Does not calculate hoop stress, radial stress, burst speed, containment energy, fatigue, balance grade, bearing losses, windage, gyroscopic loading, or shaft stresses.
02Does not account for spokes, hubs, nonuniform density, composite layups, shrink fits, cracks, keyways, bolt holes, or temperature effects.
03High-speed flywheels can be dangerous stored-energy devices. Use qualified engineering review, material allowables, containment, and applicable standards before building hardware.
04Custom inertia mode assumes the entered I value already represents the complete rotating assembly about the correct axis.

References

[1]
Flywheels - Kinetic Energy
Engineering ToolBox
Reference for E = 1/2 I omega^2, angular velocity conversion, and inertia shape factors.
[2]
Flywheel Energy & Burst-Speed Calculator
Eng Bench
Reference for stored energy, thick-ring inertia, rim speed, and the importance of stress/burst-speed checks.
[3]
Flywheel Energy Calculator
MachineCalcs
Reference for calculator UX: solid disk, thick ring, thin rim, moment of inertia, rim speed, and angular speed outputs.

Frequently Asked Questions

What is the flywheel energy formula?

Flywheel energy is E = 1/2 I omega^2, where I is moment of inertia and omega is angular speed in rad/s. RPM must be converted with omega = 2 pi n / 60.

Why does RPM matter so much?

Energy is proportional to omega squared. If the flywheel geometry and mass stay the same, doubling RPM stores four times as much energy.

Which inertia model should I choose?

Use solid disk for a uniform disk, thick ring for an annular flywheel with a significant bore, thin rim when most mass is concentrated near the outside radius, and custom inertia when a CAD model or datasheet gives I directly.

How is this different from the Kinetic Energy Calculator?

The Kinetic Energy Calculator handles straight-line motion with KE = 1/2 mv^2. This calculator handles rotating bodies, so it needs moment of inertia and angular velocity.

Can rim speed tell me if a flywheel is safe?

No. Rim speed is only an early warning signal. Safe flywheel design needs material stress, burst-speed, fatigue, balancing, containment, and bearing checks.

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