Moment of Inertia Calculator

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Radius r for disks/spheres/hoops; full length L for rods; outer radius r2 for hollow cylinder; major radius R for torus; width b for rectangular plate.
Shifts the axis from the centre of mass to a parallel axis at distance d. Adds m*d^2.
Provide angular velocity and/or acceleration to compute kinetic energy and torque.
Moment of inertia (primary axis)
0.25kg·m²
Moment of inertia (secondary axis)0.125kg·m²
Primary axis0.25
Secondary axis0.125

This solid disk has a moment of inertia of 0.25 kg·m² about its primary axis.

  • Doubling the primary dimension from 0.5 m to 1 m would quadruple the moment of inertia to about 1 kg·m², because inertia scales with the square of distance.
  • Doubling the mass to 4 kg would double the result to 0.5 kg·m², because inertia scales linearly with mass.
  • The primary (spin) axis gives 0.25 kg·m² while the secondary (tipping) axis gives 0.125 kg·m² - a ratio of 2:1. The spin axis is usually smaller because mass is distributed closer to it.

Next stepToggle "Apply parallel-axis theorem" to shift the rotation axis away from the centre of mass, or enable angular dynamics to compute torque and kinetic energy.

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