Physics

Flywheel Energy Calculator

Calculate kinetic energy stored in a rotating flywheel.

Educational use only Physics

Flywheel Energy Calculator estimates kinetic energy stored in a rotating flywheel from either direct moment-of-inertia and angular-velocity inputs or derived shape, mass, radius, and RPM values. Use it for physics labs, machine-design screening, energy-storage comparisons, regenerative-braking examples, and sanity checks on rotating assemblies. The calculation uses E = 1/2 I omega^2, so energy rises linearly with moment of inertia and with the square of angular speed. Results depend strongly on geometry, units, speed, material limits, and containment assumptions, so treat the output as planning or education support before any real mechanical design.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

How to use this tool

Choose the calculation mode based on whether you know moment of inertia directly or need it derived from shape, mass, and radius.
Enter flywheel shape, mass, radius, rotational speed, moment of inertia, or angular velocity as applicable.
Run the calculator and review the stored kinetic energy output.
Validate stresses, speed limits, and containment requirements separately before applying the result to physical hardware.

Flywheel Parameters

Calculation Mode

Derived From Shape, Mass & Speed Direct From I & ω

Flywheel Shape

Mass (kg)

Radius (m)

Rotational Speed (RPM)

Stored Kinetic Energy

Ready to spin up the calculations!

Enter flywheel parameters to see stored energy.

Flywheel Energy Storage

Energy in Rotation

A flywheel stores energy in rotational motion. Rotational kinetic energy equals one half times moment of inertia times angular speed squared. The moment of inertia captures how mass is distributed relative to the axis; mass farther from the axis stores more energy for the same angular speed.

Because energy scales with angular speed squared, increasing speed is powerful. Doubling rotational speed quadruples stored energy, assuming the flywheel can safely handle the stress.

Strength and Safety

A spinning flywheel experiences large tensile stresses. At high speeds, material strength becomes the limiting factor. If a flywheel fails, fragments can carry enormous energy, so containment is a serious design requirement.

Materials with high strength-to-density ratios are valuable. Composite flywheels can spin faster than many metal designs, but they have their own manufacturing and failure-mode considerations. Safe flywheel design is as much about stress and containment as energy capacity.

Losses and Bearings

Real flywheels lose energy through bearing friction, air drag, electrical losses, and control electronics. Vacuum housings reduce aerodynamic losses. Magnetic bearings can reduce contact friction. Motor-generator efficiency affects charge and discharge performance.

These losses determine how long a flywheel can store energy usefully. Flywheels are often excellent for short-duration power smoothing, frequency regulation, regenerative braking, and pulse power, but less attractive for long-term storage where self-discharge matters.

Power Versus Energy

Flywheels can often deliver high power quickly, but their total energy capacity may be modest compared with chemical batteries or fuel. This distinction makes them useful where rapid cycling and high power are more important than many hours of storage.

Applications include grid stabilization, uninterruptible power systems, rail and industrial energy recovery, and laboratory systems. The best use cases match the flywheel's strengths: fast response, high cycle life, and repeated charge-discharge events.

Formula or method

Stored rotational energy is calculated as E = 1/2 * I * omega^2.
In derived mode, a solid disk uses I = 1/2 * m * r^2 and a thin rim uses I = m * r^2.
RPM is converted to angular velocity with omega = rpm * 2*pi / 60.

Worked example

Comparing disk and rim assumptions

Mode: derived
Shape: solid disk
Mass: 10 kg
Radius: 0.5 m
Rotational speed: 3000 RPM

Result: The calculator derives moment of inertia, converts RPM to angular velocity, and reports stored energy in joules, kilojoules, and watt-hours.

Switching the shape to a thin rim increases moment of inertia for the same mass and radius, which increases stored energy, but real rim designs also need material stress and containment checks.

How to interpret the result

Flywheel energy is highly sensitive to speed and mass distribution, so a plausible number still needs engineering context.

Doubling RPM quadruples stored energy if moment of inertia stays the same.
Moving mass farther from the axis increases moment of inertia and stored energy for the same mass.
Watt-hours make flywheel energy easier to compare with batteries, but power delivery and self-discharge are separate questions.
High stored energy also means higher failure consequence, so containment and material limits matter.

Common mistakes

Entering RPM in the angular-velocity field instead of rad/s when using direct mode.
Assuming the solid-disk or thin-rim model matches a real flywheel with spokes, hubs, shafts, or nonuniform geometry.
Comparing watt-hours without considering power rating, losses, and discharge duration.
Ignoring hoop stress, overspeed margin, bearings, vibration, and containment.

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Models are idealized and may ignore drag, friction, nonlinearity, and measurement error.

Formula References

SI-unit forms of classical mechanics and wave equations.
Idealized models unless explicitly stated otherwise.

Assumptions

Derived mode assumes an ideal solid disk or thin rim with uniform mass distribution.
{"Inputs use SI units"=>"kilograms, meters, radians per second, and RPM as labeled."}
Energy calculation is ideal and does not subtract bearing, aerodynamic, motor-generator, or control losses.

Review note and limitations

Method - ideal rotational kinetic energy from moment of inertia and angular velocity.

Does not calculate hoop stress, burst speed, fatigue, bearing load, gyroscopic effects, rotor dynamics, thermal effects, or containment requirements.
Does not validate whether a material, shaft, bearing, enclosure, or motor-generator can safely operate at the entered speed.

Physics and early design aid only. Validate material strength, stress, balance, containment, bearings, controls, and safety factors before applying results to a physical flywheel.

FAQ

Why does RPM affect flywheel energy so strongly?

Rotational energy scales with angular velocity squared, so a small increase in speed can produce a much larger increase in stored energy.

Should I use solid disk or thin rim mode?

Use solid disk for a uniformly filled disk or cylinder approximation, and thin rim when most mass is near the outside radius. Real flywheels may need a custom moment of inertia.

Can this determine whether a flywheel is safe?

No. Safety depends on material stress, burst speed, fatigue, balance, bearings, containment, controls, and applicable standards, none of which are solved here.

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