THE NUMORIX GUIDE
How to use the Moment of Inertia Calculator
Last reviewed September 14, 2026
What this calculator does
The engine uses I = k m r^2, with k = 1 for a point mass or thin ring, k = 0.
Formula and method
The engine uses I = k m r^2, with k = 1 for a point mass or thin ring, k = 0.5 for a solid disk, and k = 0.4 for a solid sphere about its center. It returns only the moment of inertia in the visible result.
Variables and inputs
Mass m is in kilograms, radius r in meters, and shape is Point Mass, Ring, Disk, or Sphere. The default is m = 5 kg, r = 0.5 m, and Disk; the UI requires positive mass and radius.
Worked example
For a 5 kg disk with radius 0.5 m: I = 0.5(5)(0.5^2) = 0.625 kg*m^2. Choosing a ring with the same mass and radius would give I = 1(5)(0.5^2) = 1.25 kg*m^2.
How to interpret the result
Moment of inertia measures resistance to angular acceleration around a specified axis. For the same mass and outer radius, mass concentrated farther from the axis produces a larger value.
Common mistakes to avoid
Use radius rather than diameter, and choose a shape whose mass distribution and rotation axis match the object. A solid sphere's 0.4 factor is not the factor for a thin spherical shell, and a disk factor assumes rotation about its central symmetry axis.
Assumptions and limitations
These are simplified rigid-body formulas and do not account for thickness, nonuniform density, an offset axis, or composite parts. The engine has no angular-velocity input, so its kineticEnergy and angularMomentum fields remain zero rather than being calculated from I.