What formulas are used for each shape?

Solid disk: I = ½MR². Hollow disk: I = ½M(R_o² + R_i²). Thin ring: I = MR². Spoke wheel: I_rim + I_hub + I_spokes, where spokes are treated as thin rods rotating about one end (I = ⅓mL²).

How does a hollow disk store more energy than a solid disk of the same mass?

Mass at a larger radius contributes more to I because inertia scales with r². Moving mass outward — as in a hollow disk or rim — raises I without adding weight, storing more energy per kilogram at the same speed.

What is angular momentum and why does it matter?

Angular momentum L = Iω. A flywheel with high L resists changes to its spin axis (gyroscopic effect) and smooths out torque fluctuations in crankshaft-driven machines. High L is desirable for energy buffering; it can be undesirable in vehicle handling if misaligned.

Why does the hollow-disk formula use (R_o² + R_i²) not (R_o² − R_i²)?

The hollow-disk (annular cylinder) formula I = ½M(R_o² + R_i²) accounts for the actual mass distribution of the remaining material. The (R_o² − R_i²) term appears when you integrate over the full annular cross-section in cylindrical coordinates, which then simplifies to the ½M(R_o² + R_i²) form after substituting M = ρπt(R_o² − R_i²).

What units does this calculator use?

Inputs accept kg or lb for mass, and m/cm/mm/in for length. All values are converted to SI (kg, m, rad/s) before calculation. Moment of inertia is output in kg·m², energy in Joules (with kJ and Wh), and angular momentum in kg·m²/s.

Flywheel Inertia Calculator

Name: Flywheel Inertia Calculator
Availability: InStock
Author: Nham Vu

Calculate the moment of inertia and stored kinetic energy of a flywheel for solid disk, hollow disk, thin ring, or spoke-wheel geometry.

Flywheel Geometry

Geometry

Total mass

Outer radius

Rotational speed

Enter geometry and speed, then click Calculate

Summary

Calculate the moment of inertia and stored kinetic energy of a flywheel for solid disk, hollow disk, thin ring, or spoke-wheel geometry.

How it works

Select the flywheel geometry that matches your design: solid disk, hollow disk, thin ring, or spoke wheel.
Enter the mass and required dimensions (outer radius, inner radius, spoke count, etc.).
Enter the rotational speed in RPM or rad/s.
Click Calculate to see moment of inertia, stored kinetic energy, and angular momentum.
The formula panel shows every substitution so you can verify the result by hand.

Use cases

Sizing flywheel geometry for a target moment of inertia in engine design.
Comparing solid-disk vs. hollow-disk vs. rim-weighted designs at equal mass.
Computing angular momentum for gyroscopic stability analysis.
Estimating stored energy in punch-press or stamping-machine flywheels.
Validating finite-element results against closed-form inertia formulas.
Educational exercises on rotational dynamics and parallel-axis theorem.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu