Calculate flywheel stored energy, usable energy between two speeds, and key outputs like inertia, angular speed, rim speed, and sizing estimates.
Advanced options
How to use our Flywheel Energy Storage Calculator
- Choose a value in Calculation mode to decide whether you want energy at one speed, usable energy between two speeds, or a sizing result.
- Select Flywheel shape. Use solid disk for a uniform disk, thin ring for mass concentrated near the rim, or custom inertia factor k only if you already know the correct k value.
- Enter Mass (kg), Radius (m), and Maximum speed (rpm). If you change the unit selectors in Advanced options, enter the mass and radius in those selected units.
- For usable-energy mode, also enter Minimum speed (rpm). This lower speed must be less than Maximum speed (rpm).
- If you picked custom geometry, enter Inertia factor k (unitless). Common reference values are 0.5 for a solid disk and 1 for a thin ring.
- Click Calculate to see the main result plus context outputs such as Moment of inertia, Angular speed, Rim speed, and energy in kWh.
- Sanity-check the result: if Flywheel shape changes from solid disk to thin ring while mass, radius, and speed stay the same, the energy should increase because more mass is farther from the center.
- Use the result labels carefully: Stored rotational energy is total ideal energy at one speed, while Usable energy between speeds is only the energy available as the flywheel slows from the higher speed to the lower speed.
Definitions
Calculation mode: The type of problem you want to solve, such as total stored energy at one speed or usable energy between two speeds.
Moment of inertia: A measure of how strongly the flywheel resists changes in its rotation. It depends on both mass and how far that mass is from the center [3].
Angular speed: How fast something spins, measured here in radians per second. The calculator converts from rpm before using the energy formula [1].
Stored rotational energy: The kinetic energy in the spinning flywheel, computed from moment of inertia and angular speed using the standard rotational-energy relationship [1][4].
Usable energy between speeds: The energy available when the flywheel slows from Maximum speed (rpm) to Minimum speed (rpm). This is often less than the total stored energy at top speed.
Inertia factor k: A shape factor in the model I = k m r^2. In this calculator, k is 0.5 for a solid disk, 1 for a thin ring, or a custom positive value you enter.
Rim speed: The linear speed of the flywheel edge. It equals angular speed times radius and can help you judge how extreme a design is.
Common mistakes and quick fixes
Mistake: Using Stored energy at one speed when you really want the energy released from slowing down.
Fix: Switch Calculation mode to the usable-energy option and fill in both Maximum speed (rpm) and Minimum speed (rpm) .
Mistake: Entering Minimum speed (rpm) equal to or higher than Maximum speed (rpm) .
Fix: Make Minimum speed (rpm) smaller than Maximum speed (rpm) so Usable energy between speeds is positive.
Mistake: Changing Mass unit for input/output or Radius unit for input/output but leaving the number in old units.
Fix: Re-enter Mass (kg) and Radius (m) using the currently selected unit system so the calculator converts them correctly.
Mistake: Picking Custom inertia factor k but forgetting to enter a positive Inertia factor k (unitless) .
Fix: Enter a value greater than 0, or change Flywheel shape back to solid disk or thin ring.
Mistake: Assuming Energy in kWh is an electrical output from a real machine.
Fix: Read it as an ideal mechanical-energy equivalent of Stored rotational energy or Usable energy between speeds , not a guaranteed wall-plug energy delivery.
Mistake: Interpreting a very high Rim speed as automatically safe just because the math works.
Fix: Treat Rim speed as a context output only and use real engineering design checks for material stress, containment, and losses.
Limitations & Key Assumptions / Boundary Conditions
- Results are ideal mechanical values. They do not include bearing friction, motor-generator losses, windage, vacuum losses, or control-system losses.
- The geometry model is simplified to a solid disk, a thin ring, or a custom inertia factor k. Real flywheels can have more complex mass distribution.
- This tool does not perform stress, burst-speed, fatigue, containment, or safety certification checks. A high Rim speed may indicate a demanding design, but it is not a pass/fail safety result.
- Minimum speed (rpm) must be less than Maximum speed (rpm) in usable-energy mode, or the result is physically invalid for discharge.
- Unit selectors apply to the values you enter for Mass (kg) and Radius (m). If you change units without updating the numbers, the output will be wrong.
- Sizing results depend completely on the chosen target-energy basis in the calculator build. If a target-energy input is not part of your active interface, solve modes may not be usable in practice.
Methodology
Core equations
The calculator first finds the flywheel's moment of inertia from a simple shape model, then converts rpm to angular speed, then computes rotational energy. Rotational kinetic energy is given by one-half times moment of inertia times angular speed squared [1][4].
I = k * m * r^2
ω = 2 * π * rpm / 60
E = 0.5 * I * ω^2
ΔE = 0.5 * I * (ωmax^2 - ωmin^2)
v = ω * r
kWh = J / 3600000
Shape factor used
For the simplified model, the calculator uses k = 0.5 for a solid disk and k = 1 for a thin ring. A custom positive k lets you match another known inertia model more closely.
How each mode is interpreted
Stored energy at one speed uses the selected Maximum speed (rpm) as the operating speed and reports total ideal rotational energy at that speed.
Usable energy between two speeds subtracts the lower-speed energy from the higher-speed energy, so it represents the energy released during slowdown rather than the total energy at top speed.
Solve mass and Solve radius come from rearranging the same energy equation.
m = 2 * E / (k * r^2 * ω^2)
r = sqrt(2 * E / (k * m * ω^2))
Mini example
Suppose you choose a solid disk with mass 10 kg, radius 0.2 m, and maximum speed 3000 rpm. Then I = 0.5 * 10 * 0.2^2 = 0.2 kg m^2. Angular speed is about 314.16 rad/s. Stored energy is 0.5 * 0.2 * 314.16^2 = about 3947.84 J. If the flywheel slows to 1500 rpm, the usable energy becomes about 2960.88 J.
Assumptions behind the outputs
This method assumes a rigid flywheel with a fixed inertia factor, ideal energy storage, and no losses during charging, spinning, or discharge. Real systems can deliver less usable output because of friction, electrical conversion losses, and safety speed limits.