# Flywheel Energy Storage Calculator Calculate the kinetic energy stored in a flywheel. E = ½·I·ω², ω = 2π·n/60. Enter the moment of inertia directly, or compute it from flywheel mass and radius (I = ½·m·r²). Supports J/kJ/Wh. > Canonical page: https://elysiatools.com/en/tools/flywheel-energy-storage - **Category:** Math & Numbers - **Keywords:** flywheel, kinetic energy, moment of inertia, energy storage, angular velocity, rotational energy, mechanical engineering ## Overview The Flywheel Energy Storage Calculator computes the kinetic energy stored in a rotating flywheel using its moment of inertia and rotational speed. It supports direct input of the moment of inertia or automatically derives it from the flywheel's mass and radius, outputting results in Joules, Kilojoules, or Watt-hours. ## Inputs - **Moment of Inertia I (kg·m²)** (number): Optional. If omitted, it is computed from flywheel mass and radius using I = ½·m·r². - **Rotational Speed n (rpm)** (number): e.g. 3000 - **Flywheel Mass m (kg)** (number): Optional. Used with radius to derive I when I is not provided. - **Flywheel Radius r (m)** (number): Optional. Used with mass to derive I when I is not provided. - **Energy Unit** (select) - **Decimal Places** (number) ## When to use - Designing mechanical energy storage systems that rely on rotating flywheels. - Calculating the kinetic energy capacity of a flywheel when only its mass, radius, and rotational speed are known. - Converting rotational speed and moment of inertia into standard energy units like Joules, Kilojoules, or Watt-hours. ## How it works - Enter the rotational speed in revolutions per minute (rpm). - Provide the moment of inertia directly, or input the flywheel's mass and radius to let the calculator compute it using the formula I = ½·m·r². - Select your preferred energy unit (J, kJ, or Wh) and set the desired decimal precision. - Click calculate to obtain the angular velocity and total stored kinetic energy. ## Use cases - Determining the energy storage capacity of industrial UPS systems utilizing mechanical flywheels. - Sizing flywheels for automotive regenerative braking systems by analyzing mass and rotational speed limits. - Academic physics and mechanical engineering calculations involving rotational dynamics and energy conservation. ## Frequently asked questions ### How does the calculator compute the moment of inertia if I do not provide it? It calculates the moment of inertia using the formula I = ½·m·r², assuming a solid cylinder or disk shape based on the mass and radius you provide. ### What units of energy does this tool support? The calculator supports Joules (J), Kilojoules (kJ), and Watt-hours (Wh). ### What formula is used to calculate the stored kinetic energy? It uses the rotational kinetic energy formula E = ½·I·ω², where I is the moment of inertia and ω is the angular velocity in radians per second. ### How is rotational speed in rpm converted to angular velocity? Rotational speed (n) in rpm is converted to angular velocity (ω) in rad/s using the formula ω = 2π·n/60. ### Can I adjust the precision of the output? 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