A flywheel stores rotational kinetic energy. It can absorb energy while speeding up and release energy while slowing down, helping buffer variations in torque or load. For a fixed moment of inertia, energy is proportional to speed squared. This calculator compares two speeds as energy ratios; it does not calculate joules or size a rotor.
Flywheel Interactive Calculator
Vary the starting and final RPM to see how flywheel stored energy changes with speed squared.
Equation Used
For the same flywheel, moment of inertia stays constant, so stored rotational energy changes only with speed squared. Doubling RPM gives four times the stored energy.
- Same flywheel, so moment of inertia I is unchanged.
- Losses, bearing drag, and material stress limits are not included.
- Energy is normalized to 1 at a positive starting RPM. There is no inertia input, so outputs are ratios rather than joules. A zero starting speed has no valid relative-energy ratio.
Energy exchanged as speed changes
For rotation about a fixed axis, stored energy is E = ½Iω². Moment of inertia I depends on mass and its distribution about that axis. More mass farther from the axis increases I, but rotor geometry also affects strength and support loads.
A flywheel does not create energy. Its speed rises when net input work is positive and falls when it supplies net work to the connected machine. Bearings, air drag and other losses reduce energy available to the load.
The usable energy between two specified speeds is the difference between their stored energies. Energy at the higher speed is not all usable if the machine must stay above a minimum speed.
Buffering changes in power
Flywheels are used to smooth cyclic machine motion and supply short-duration energy demands. Mechanical drives exchange that energy through a shaft; electrical storage systems use a motor-generator and power electronics.
Beacon Power is one example of a manufacturer of grid-scale flywheel storage. Its complete systems include controls and supporting equipment beyond a rotating mass. A simple energy ratio does not predict the power, duration or performance of such a system.
Energy ratio for the same rotor
For a fixed I and positive starting speed n1, E2/E1 = (n2/n1)². The RPM-to-radians conversion cancels because the same units are used for both speeds.
The calculator sets the base energy ratio to 1. Final energy ratio is (n2/n1)², and percentage energy change is 100[(n2/n1)² − 1]. A negative change means less stored energy, not negative absolute energy.
Absolute energy requires I: E = ½I(2πn/60)². Ideal energy released while slowing from nhigh to nlow is ½I[(2πnhigh/60)² − (2πnlow/60)²], before losses. Neither inertia nor losses is entered here.
Starting speed must be greater than zero for this ratio interpretation. An energy ratio cannot be calculated from a stationary start because its initial energy is zero. An absolute-energy calculation requires the moment of inertia.
Example: doubling or reducing speed
Set start speed to 1,000 RPM and final speed to 2,000 RPM. Speed ratio is 2, base energy ratio is 1, final energy ratio is 4 and energy change is +300%.
Set final speed to 500 RPM while retaining the 1,000 RPM start. The final energy ratio becomes 0.25 and the change is −75%. Three quarters of the initial rotational energy has been removed from the rotor; the fraction delivered usefully depends on losses.
If speed falls to 90% of its starting value, remaining energy is 81% and the ideal decrease is 19%. These comparisons do not establish a permissible speed range, press-stroke capacity or recharge time.
Energy arithmetic is only part of rotor design
Rotor stress, defects, fatigue, balance, bearings, attachments, controls and containment must be considered for a real flywheel. A material name alone does not establish a safe rim speed, and a simple yield-stress calculation is not a burst-speed qualification.
Recharge time depends on available net power. Added inertia can smooth continuous cyclic motion but also increases torque needed for acceleration. Compare complete systems for the intended duty rather than treating a high energy ratio as proof of suitability.
This calculator gives no fabrication dimensions, balance grade, containment design or operating-speed approval.
Frequently asked questions
Are the energy outputs in joules?
No. The starting energy is normalized to 1 and the final value is a ratio. Absolute energy needs the rotor’s moment of inertia.
Why does double speed give four times the energy?
For unchanged moment of inertia, rotational energy is proportional to angular speed squared.
Is +300% the same as four times the initial energy?
Yes. The increase is three times the initial value, leaving a final total of four times that value.
Can all stored energy be used in one machine stroke?
Only if the rotor can slow to zero, ignoring losses. Most applications have a permitted minimum speed, so usable energy is the difference between two operating states.
Can I compare from a stationary start?
Not as an energy ratio: the initial energy is zero, so division by it is undefined. Use an absolute-energy calculation with known inertia instead.
Does a negative energy change mean the flywheel rotates backward?
No. It means the final entered speed is lower and the rotor stores less energy. These inputs use nonnegative speed magnitudes.
Does this tool check burst speed or rotor strength?
No. Structural and dynamic qualification require geometry, material data and a complete engineering assessment not included here.
Further reading
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
