Flywheel Energy Storage Calculator
Enter the flywheel mass, radius, and rotational speed to get the stored kinetic energy, moment of inertia, angular velocity, and rim surface speed. Choose from five standard flywheel geometries (solid disk, hollow disk, rim-loaded wheel, solid sphere, thin hollow cylinder), switch between metric and imperial units, and optionally add material tensile strength and density to find the theoretical specific energy limit. All outputs update instantly as you type.
How flywheel energy storage works
A flywheel stores kinetic energy by spinning a rotor at high speed. When energy is put in (from a motor or generator), the rotor accelerates; when energy is extracted, the rotor slows. Because kinetic energy scales with the square of angular velocity (E = 0.5 I omega squared), doubling the rotational speed quadruples the stored energy. This makes flywheels well suited to applications that need rapid charge and discharge cycles, such as frequency regulation on power grids, uninterruptible power supplies (UPS), regenerative braking in rail vehicles, and energy recovery in motorsport.
The geometry constant k and flywheel shapes
The moment of inertia is I = k m r squared, where k is a dimensionless constant that depends only on how the mass is distributed. A rim-loaded wheel (k = 1.0) concentrates all mass at the outer edge and is the most energy-dense geometry for a given mass and radius. A flat solid disk has k = 0.606 because much of its mass sits close to the axis. A hollow flat disk or thin hollow cylinder falls between the two. A solid sphere has k = 0.4. Choosing the right geometry is the first design decision: for the same mass and radius, a rim-loaded wheel stores 65 percent more energy than a solid disk.
Surface speed and material limits
Flywheel design is ultimately limited by tensile strength, not geometry. As the rim spins faster, centrifugal stress at the outer edge rises with the square of the rim speed. The theoretical maximum specific energy a material can deliver is E/m = k sigma / rho, where sigma is tensile strength and rho is density. This is why carbon fibre composites (high sigma, low rho) achieve specific energies of around 200 to 300 Wh/kg, far beyond steel (roughly 50 Wh/kg). Modern carbon fibre flywheels spinning at 50,000+ RPM in evacuated housings now rival lithium-ion batteries in specific energy while offering much longer cycle life and faster charge-discharge.
Flywheel vs. battery storage - when to choose a flywheel
Flywheels excel where batteries struggle: very high cycle life (millions of cycles vs. a few thousand for lithium-ion), high power density, fast response (milliseconds), and no degradation with temperature or depth-of-discharge. Their drawback is self-discharge - a flywheel running in air loses energy to friction and windage in minutes to hours. Magnetic-bearing, vacuum-enclosed flywheels extend this to 24 hours or more, making them practical for grid-scale frequency regulation and UPS, though not for long-duration storage. For short-burst, high-power applications such as crane energy recovery or racecar KERS, a flywheel is often the best choice.
Common flywheel materials - typical properties
| Material | Tensile strength (MPa) | Density (kg/m³) | Specific energy* (Wh/kg) |
|---|---|---|---|
| Steel (high-strength) | 1500 | 7800 | ~53 |
| Aluminium alloy | 500 | 2700 | ~51 |
| Carbon fibre composite | 1500 | 1600 | ~260 |
| Glass fibre composite | 800 | 2000 | ~111 |
| Titanium alloy | 1000 | 4500 | ~62 |
| Cast iron | 250 | 7200 | ~10 |
Approximate tensile strength, density and theoretical specific energy for common flywheel materials. Actual values vary by grade and heat treatment.
Frequently asked questions
What is the formula for flywheel energy storage?
The stored kinetic energy is E = 0.5 * I * omega squared, where I is the moment of inertia (kg m squared) and omega is the angular velocity in radians per second. The moment of inertia depends on the flywheel geometry: I = k * m * r squared, where k is the geometric constant (ranging from 0.333 for a hollow disk to 1.0 for a rim-loaded wheel), m is mass, and r is the outer radius.
How does rotational speed affect stored energy?
Energy scales with the square of angular velocity, so doubling the RPM stores four times as much energy. This is why high-speed flywheels (50,000 to 100,000 RPM) can achieve useful energy densities despite moderate physical size. Increasing the radius is less effective: energy scales with r squared through the inertia term, but material stress at the rim also scales with r squared, so the advantage is offset by the material limit.
What is the geometric constant k?
The geometric constant k (also called the shape factor) describes how mass is distributed relative to the axis of rotation. A value of 1.0 means all the mass is at the outer radius (rim-loaded wheel); lower values mean more mass is distributed closer to the axis. A flat solid disk has k = 0.606, a hollow disk (thin rim) has k = 0.333, a thin hollow cylinder has k = 0.5, and a solid sphere has k = 0.4. Higher k means more energy for the same mass and radius.
How do I convert flywheel energy from joules to watt-hours?
Divide the energy in joules by 3600 (there are 3600 seconds in an hour, and one watt-hour equals one joule per second for one hour). For example, 360,000 J equals 100 Wh or 0.1 kWh. This calculator shows both units so you can compare flywheel storage against battery specifications, which are typically quoted in Wh or kWh.
What materials are best for flywheels?
The theoretical specific energy limit is E/m = k * sigma / rho, where sigma is tensile strength and rho is density. A high ratio of tensile strength to density is the key material property. Carbon fibre composites have the best ratio (specific energy up to 300 Wh/kg), followed by glass fibre, then titanium and high-strength steel (around 50 Wh/kg). Cast iron and plain steel are used only in low-speed industrial flywheels where energy density is not a priority and cost dominates.
What is the rim surface speed and why does it matter?
The rim surface speed (v = omega * r) is the tangential velocity of the outermost point of the flywheel. It determines the centrifugal stress at the rim, which is proportional to v squared times density. Steel flywheels are typically limited to rim speeds of 200 to 400 m/s; carbon fibre flywheels can operate up to 800 to 1000 m/s in vacuum chambers. Exceeding the material limit causes catastrophic failure, so rim speed is a primary safety constraint in flywheel design.