Flywheel Energy Calculator
Stored energy, inertia, and rim speed from rotor size.
What it does
Flywheels bank energy in spin for presses, grid storage, and old farm engines alike. Speed matters most because energy climbs with its square, while radius helps twice: once in inertia and again in rim speed.
The tool above takes rotor mass, radius, and rpm for a solid disc. It returns stored energy with inertia and rim speed beside it, in kilojoules from either unit system.
The metric defaults (10 kg, 20 cm, 3000 rpm) store 9.87 kJ with rim speed 62.8 m per s. The imperial mirror (22.05 lb, 7.87 in) gives 9.86 kJ with the same rim speed.
The line follows OpenStax University Physics rotational energy with the thin disc inertia derivation beside it: half I omega squared with I as half m R squared. Maricopa college physics mirrors the same formulas and table.
How to use
- Pick imperial (lb, in) or metric (kg, cm).
- Enter rotor mass.
- Enter rotor radius, never diameter.
- Enter rpm.
- Read stored energy first.
- Read rim speed for stress sense.
Formula
- w
- Angular speed in radians per second.
- I
- Solid disc inertia in kg m2.
- E
- Stored energy in joules (kJ shown).
- r
- Rotor radius in meters inside the math.
Solid uniform disc only; hoops, spokes, and hubs carry different inertia factors. Real rotors quit at burst speed with bearings and balance long before textbook energy, so rim speed reads as a stress hint.
Worked example
Example: 10 kg disc, 20 cm, 3000 rpm
Metric defaults: 10 kg, 20 cm radius, 3000 rpm.
- Inertia: 0.5 x 10 x 0.04 = 0.2 kg m2.
- Speed: 3000 x 2pi/60 = 314.16 rad/s.
- Energy: 0.5 x 0.2 x 314.16^2 = 9869.6 J.
- kJ: 9869.6 / 1000 = 9.87 kJ.
- Rim: 314.16 x 0.2 = 62.8 m per s.
- Tool shows 9.87 kJ, 0.2 kg m2, 62.8 m per s. Imperial mirror gives 9.86 kJ.
Reference table
| Rotor | Energy | Rim |
|---|---|---|
| 10 kg, 20 cm, 3000 rpm | 9.87 kJ | 62.8 m per s |
| 5 kg, 10 cm, 6000 rpm | 4.93 kJ | 62.8 m per s |
| 22.05 lb, 7.87 in, 3000 rpm | 9.86 kJ | 62.8 m per s |
Limits
- Solid disc shape only.
- Burst speed and bearings rule reality.
- Balance and vibration ignored.
- Motor and drag losses excluded.
Common mistakes
- Entering diameter as radius.
- Forgetting rpm to rad/s conversion.
- Expecting double speed to double energy.
- Sizing storage without burst margin.
- Mixing grams with kilograms.
Try it yourself
Quick checks. Answers sit tucked under each question.
5 kg, 10 cm, 6000 rpm?
4.93 kJ with 62.8 m per s rim.
Double the speed?
Four times the energy; E follows w squared.
Diameter entered by mistake?
Halve it first; radius is what the math wants.
Questions
What is flywheel energy formula?
Half I w squared, with solid disc I as half m r squared.
Speed or mass for storage?
Speed wins by square; radius helps twice.
What limits real flywheels?
Rim burst stress, bearings, balance, and containment.
kJ vs Wh?
Divide kJ by 3.6 for Wh; 9.87 kJ is 2.74 Wh.
Hoop instead of disc?
Hoop inertia is m r squared, double the disc, so more storage per mass.
Why rim speed shown?
Stress follows rim speed squared, so it hints how close to limits.