Formula and Method for Flywheel Energy Storage
A flywheel stores energy as rotational kinetic energy: E = ½Iω², where I is the rotor's moment of inertia (kg·m²) and ω is its angular velocity in radians per second. Because ω depends on the square of rotational speed, doubling the RPM quadruples the stored energy — speed matters far more than mass or radius for energy density. This calculator finds the total kinetic energy at your maximum speed and the usable energy that is actually released as the flywheel spins down to a minimum operating speed, since most flywheel systems never discharge all the way to zero RPM.
How the calculation works
The calculator first converts your mass and radius to kilograms and meters, then picks a moment-of-inertia formula based on the flywheel's shape: I = ½mr² for a solid disk or cylinder with mass spread evenly through the rotor, or I = mr² for a thin-walled rim or hoop where nearly all the mass sits at the outer radius (a rim-weighted flywheel stores twice the energy of a solid disk of the same mass, radius, and speed). Each RPM value is converted to angular velocity with ω = RPM × 2π / 60, then the total energy at maximum speed is Emax = ½Iωmax², the energy remaining at minimum speed is Emin = ½Iωmin², and the usable stored energy is the difference, ΔE = Emax − Emin.
Getting accurate results
- Use radius, not diameter: if you measured across the flywheel, divide by 2 before entering the radius — using the diameter by mistake overstates stored energy by 4×, since energy scales with r².
- Pick the shape that matches your rotor: a solid disk (I = ½mr²) is the conservative estimate, while a rim-heavy design (I = mr²) is the optimistic one — use whichever your flywheel's mass distribution resembles more closely.
- Minimum speed sets the usable fraction: a flywheel that only discharges from 100% to 50% speed releases 75% of its total stored energy (1 − 0.5²), not 50% — because energy scales with ω², shallow discharge ranges recover most of the energy.
- Check tip speed and material limits separately: this calculator assumes the rotor holds together at the entered RPM; real designs are capped by hoop stress at the rim, which depends on material strength and density, not on this formula.
Frequently Asked Questions
What is the formula for flywheel energy storage?
Stored rotational kinetic energy is E = ½Iω², where I is the moment of inertia in kg·m² and ω is angular velocity in radians per second (ω = RPM × 2π / 60). The moment of inertia itself depends on shape: I = ½mr² for a solid disk or cylinder, or I = mr² for a thin-walled rim or hoop.
Why does the calculator show a "usable" energy that's less than the total?
A flywheel is rarely discharged all the way to a stop — most systems keep spinning down to a minimum operating speed so the generator, bearings, or control electronics keep working. The usable energy is the difference between the energy at maximum speed and the energy at that minimum speed: ΔE = ½I(ωmax² − ωmin²). Since energy scales with the square of speed, even a modest speed drop releases a large share of the stored energy.
Why does flywheel shape change the result so much?
Moment of inertia depends on how far the mass sits from the axis of rotation. A thin rim or hoop concentrates all its mass at the outer radius (I = mr²), while a solid disk of the same mass and radius spreads the mass evenly and stores only half as much energy at the same speed (I = ½mr²). This is why flywheel-battery designs often use rim-weighted or composite rotors to maximize energy density.
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |