Flywheels store energy as rotation. Modern carbon-fibre flywheels spinning at tens of thousands of rpm smooth power grids, back up data centres and recover braking energy in buses and race cars. Their limit is the tensile strength of the rotor material.
How to use the Flywheel Energy Storage Calculator
- Flywheel shape
- Mass m
- Radius r
- Angular speed ω
- Tensile strength σ
- Density ρ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the shape, enter the mass, radius and speed. The material strength and density give the maximum specific energy before the rotor would burst (K is the shape factor).
Inputs explained
| Field | What to enter |
|---|---|
| Flywheel shape | Choose one: Rim-loaded wheel (I = m·r², K = 0.5), Flat solid disk (I = ½m·r², K = 0.606), Flat disk with a hole (I ≈ 0.6·m·r², K = 0.305), Solid sphere (I = 0.4·m·r², K = 0.5) … |
| Mass m | Units: kg, g, mg, t, lb, oz |
| Radius r | Units: m, cm, mm, km, in, ft … |
| Angular speed ω | Units: rpm, rad/s |
| Tensile strength σ | Units: MPa, GPa, kPa, Pa, psi, ksi |
| Density ρ | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
What each result means
- Moment of inertia = [k]×[Mass m]×[Radius r]^2
- Stored energy = [Moment of inertia]×[Angular speed ω]^2÷2
- Specific energy = [Stored energy]÷[Mass m]÷3600
- Maximum specific energy of the material = [K]×[Tensile strength σ]÷[Density ρ]÷3600
- Safety margin (max ÷ actual) = [Maximum specific energy of the material]÷[Specific energy]
Example values
How the main result changes when Mass m changes and everything else stays at the example values above:
| Mass m (kg) | Stored energy (kJ) |
|---|---|
| 50 | 1,233.7006 |
| 75 | 1,850.5508 |
| 100 | 2,467.4011 |
| 125 | 3,084.2514 |
| 150 | 3,701.1017 |
| 200 | 4,934.8022 |
Formula
E = ½·I·ω², I = k·m·r², e_max = K·σ/ρ
Worked example
Inputs — Flywheel shape: Flat solid disk (I = ½m·r², K = 0.606); Mass m: 100 kg; Radius r: 0.5 m; Angular speed ω: 6,000 rpm; Tensile strength σ: 600 MPa; Density ρ: 7,800 kg/m³.
Results — Moment of inertia = 12.5 kg·m²; Stored energy = 2,467.4011 kJ; Specific energy = 6.8539 Wh/kg; Maximum specific energy of the material = 12.9487 Wh/kg; Safety margin (max ÷ actual) = 1.889.
Key terms
- Shape factor
- A constant describing how efficiently a rotor shape uses its material strength.
Frequently asked questions
How much energy can a flywheel store?
Steel rotors reach about 5–30 Wh/kg; carbon fibre over 100 Wh/kg.
Why do flywheels spin so fast?
Energy grows with ω², so doubling speed quadruples the energy.
What limits a flywheel?
The tensile strength of the rotor – too fast and it bursts.
Why are they housed in vacuum?
To reduce air drag and losses.