Mass Moment of Inertia Calculator

Written by Great Medico

Updated September 26, 2026 •2 min read

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Problems involving mass moment of inertia can look simple until the selected geometry or axis changes the equation. This calculator keeps the shape-specific relationship explicit so the result can be checked against the standard formula.

What this calculator does

The Mass Moment of Inertia Calculator returns the rotational inertia for the selected idealized shape using the mass and the required radius or length dimensions.

How to use it

Select the object shape, then enter its mass and the radius, length, or width requested for that geometry. Keep the dimensions in the units shown on the form; supported units are converted before the equation is evaluated.

How the calculation works

The calculator now maps each supported shape to its corresponding standard centroidal-axis formula. Examples include a particle I = mr², a solid disk/cylinder I = ½mr², a thin ring I = mr², a solid sphere I = 2mr²/5, a hollow sphere I = 2mr²/3, a thin rod about its center I = mL²/12, a thin rod about one end I = mL²/3, and a rectangular plate about its center I = m(L² + W²)/12.

Example

For a solid disk with mass 2 kg and radius 0.3 m, I = ½ × 2 × 0.3² = 0.09 kg·m².

How to interpret the result

A larger mass moment of inertia means greater resistance to angular acceleration about the chosen axis. The value is axis-dependent, so do not reuse a result for a different rotation axis without applying the appropriate parallel-axis or perpendicular-axis relationship.

Limitations and notes

The built-in formulas model idealized shapes and named axes. Real objects with irregular density distributions or off-center axes may require integration, CAD-derived properties, or the parallel-axis theorem.