Calculate energy stored in a spinning flywheel using E = ½Iω². Supports different geometries, RPM-energy tables, rim speed safety analysis, and energy density comparisons.
A flywheel stores kinetic energy in its spinning mass, described by E = ½Iω², where I is the moment of inertia and ω is the angular velocity. This ancient technology — used in potter's wheels for millennia — has found modern applications in grid-scale energy storage, vehicle regenerative braking, UPS systems, and spacecraft attitude control.
The moment of inertia I depends on both the mass and how that mass is distributed relative to the rotation axis. A ring with all mass at the rim has twice the I of a solid disk of the same mass and radius, and therefore stores twice the energy at the same RPM. This is why high-performance flywheels concentrate mass at the periphery.
This calculator handles multiple flywheel geometries, computes stored energy and rim speed, and provides RPM-energy comparison tables and energy density comparisons against battery technologies. It also flags safety concerns when rim speeds approach or exceed the speed of sound.
Flywheel calculations involve moments of inertia (which differ by geometry), RPM-to-rad/s conversion, and unit conversions between joules and watt-hours. This calculator handles all geometries, generates comparison tables across RPM ranges, and provides crucial safety information about rim speeds that could cause catastrophic failure. Keep these notes focused on your operational context.
Rotational Kinetic Energy: E = ½Iω² Angular Velocity: ω = 2πn/60 Moments of Inertia: Solid cylinder/disk: I = ½mr² Hollow cylinder: I = mr² Solid sphere: I = ⅖mr² Hollow sphere: I = ⅔mr² Rim Speed: v = ωr Where: I = moment of inertia (kg·m²) ω = angular velocity (rad/s) m = mass (kg), r = radius (m)
Result: 8,333 J (2.31 Wh)
A 15 kg solid cylinder flywheel with 0.15 m radius at 3000 RPM: I = ½ × 15 × 0.15² = 0.169 kg·m², ω = 2π × 3000/60 = 314.2 rad/s, E = ½ × 0.169 × 314.2² = 8,333 J ≈ 2.31 Wh.
A flywheel energy storage system uses a motor/generator to spin up a massive rotating disk. Energy is stored as rotational kinetic energy. To extract energy, the motor operates as a generator, converting kinetic energy back to electricity as the flywheel slows down.
Modern systems use composite rotors spinning at 20,000-60,000 RPM in vacuum enclosures with magnetic bearings to minimize friction. The motor/generator is typically built into the flywheel assembly for compact design.
Grid-scale flywheel plants provide frequency regulation services, smoothing the output of wind and solar farms. The Beacon Power Stephentown facility in New York uses 200 flywheels storing 5 MWh total. In transportation, Formula 1 cars use flywheel-based KERS (Kinetic Energy Recovery Systems). NASA has explored flywheels for spacecraft energy storage as an alternative to batteries, offering longer life and higher power density.
A spinning flywheel contains enormous energy concentrated in a small volume. If the flywheel fails mechanically, the release of this energy can be explosive. This is why flywheel systems require robust containment vessels, careful material selection, and continuous monitoring of vibration and temperature. High-speed composite flywheels have a safety advantage: when they fail, the rotor tends to disintegrate into small fibers rather than large fragments.
Because E = ½Iω² and ω is proportional to RPM. Doubling the RPM quadruples the stored energy. This is why high-speed flywheels are so effective — modest increases in speed yield large energy gains.
The rim experiences centripetal stress proportional to v² (rim speed squared). If stress exceeds the material strength, the flywheel explodes catastrophically. Steel flywheels are limited to about 200-300 m/s rim speed; carbon fiber composites can reach 1000+ m/s.
Flywheels have lower energy density (1-100 Wh/kg vs 250 Wh/kg for Li-ion) but much higher power density and cycle life. They can charge/discharge in seconds and last millions of cycles without degradation.
Shapes that concentrate mass at the rim (hollow cylinder, I = mr²) have the highest moment of inertia and store the most energy for a given mass and RPM. This is why flywheel energy storage systems use rim-weighted designs.
High-speed flywheels operate in vacuum enclosures to eliminate air drag, which would otherwise dissipate energy and heat the flywheel. Low-speed flywheels (like engine flywheels) operate in air.
Modern flywheel systems with magnetic bearings and vacuum enclosures can store energy for hours with losses of 1-2% per hour. Mechanical bearing systems have higher losses and are better suited for short-duration storage.