Flywheel Moment of Inertia, Angular Momentum & Rotational Energy Calculator

Convert flywheel mass, radius, and RPM into stored joules and watt-hours.

Stored Rotational Kinetic Energy
143.9 kJ
Moment of Inertia (I = ½mr²) 2.03 kg·m²
Angular Momentum (L = Iω) 763.41 N·m·s
Stored Energy in Watt-Hours 39.97 Wh
Inputs
kg
Rotating cylinder or flywheel mass in kilograms.
m
Outer radius of the rotor in meters.
RPM
Rotational speed in revolutions per minute (RPM).
Results & Graph
Stored Rotational Kinetic Energy
143.9 kJ
Moment of Inertia (I = ½mr²)
2.03 kg·m²
Angular Momentum (L = Iω)
763.41 N·m·s
Stored Energy in Watt-Hours
39.97 Wh

Stored Rotational Kinetic Energy

Graph 1 • Rotor Mass Kg Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 kJ 116.6 kJ 233.1 kJ 50%: 71.95 kJ 72.0 50% 75%: 107.92 kJ 107.9 75% 100%: 143.9 kJ 143.9 100% 125%: 179.87 kJ 179.9 125% 150%: 215.85 kJ 215.8 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Stored Rotational Kinetic Energy 143.9 kJ Moment of Inertia (I = ½mr²) 2.03 kg·m² Angular Momentum (L = Iω) 763.41 N·m·s Stored Energy in Watt-Hours 39.97 Wh
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Stored Rotational Kinetic Energy143.9 kJMoment of Inertia (I = ½mr²)2.03 kg·m²Angular Momentum (L = Iω)763.41 N·m·sStored Energy in Watt-Hours39.97 Wh
Summary: A 45 kg solid rotor (r=0.3 m) spinning at 3600 RPM (377 rad/s) has inertia I=2.025 kg·m² and stores 143.9 kJ (39.97 Wh).
Summary: A 45 kg solid rotor (r=0.3 m) spinning at 3600 RPM (377 rad/s) has inertia I=2.025 kg·m² and stores 143.9 kJ (39.97 Wh).
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Formula & Mathematical Methodology: Rotational Energy & Inertia Physics & Engineering Equation

I = 0.5 × m × r²
ω = RPM × 2π / 60
Erot = 0.5 × I × ω²
I = 0.5 × m × r²; ω = RPM × 2π / 60; E_rot = 0.5 × I × ω²
  • rotorMassKg: Rotor Mass Kg (kg)
  • rotorRadiusM: Rotor Radius M (m)
  • rotationalSpeedRpm: Rotational Speed Rpm (RPM)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Rotational Energy & Inertia

Convert flywheel mass, radius, and RPM into stored joules and watt-hours.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: I = 0.5 × m × r²; ω = RPM × 2π / 60; E_rot = 0.5 × I × ω².
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Rotational Energy & Inertia via I = 0.5 × m × r²; ω = RPM × 2π / 60; E_rot = 0.5 × I × ω².

Frequently Asked Questions

What equation powers the Flywheel Moment of Inertia, Angular Momentum & Rotational Energy Calculator?

It evaluates I = 0.5 × m × r²; ω = RPM × 2π / 60; E_rot = 0.5 × I × ω² using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Classical Mechanics & Kinematics

Flywheel Moment of Inertia, Angular Momentum & Rotational Energy Calculator: inputs, method, and how to read the result

Convert flywheel mass, radius, and RPM into stored joules and watt-hours.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Rotor Mass Kg: Rotating cylinder or flywheel mass in kilograms.
  • Rotor Radius M: Outer radius of the rotor in meters.
  • Rotational Speed Rpm: Rotational speed in revolutions per minute (RPM).

What the calculation includes

With the default values shown, Stored Rotational Kinetic Energy is 143.9 kJ. The calculation follows Rotational Energy & Inertia Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Rotor Mass Kg from 45 kg to 50 kg changes Stored Rotational Kinetic Energy from 143.9 kJ to 159.89 kJ. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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