Second moment of area
For a rectangle about its centroidal horizontal axis, Ix = bh³ / 12. Its dimensions have units of length to the fourth power.
Calculation methodology
Know what is being calculated — and why.
Different physical quantities can have similar names. Each calculator must clearly state its quantity, reference axis, assumptions, and units.
Polar second moment of area
For perpendicular centroidal axes in a plane, J = Ix + Iy. This relationship applies to the same area and reference point.
Mass moment of inertia
Rotational inertia depends on mass distribution and has units such as kg·m². It is not the same as second moment of area.
Units and validation
Lengths must be converted consistently before evaluating formulas. Since area moments involve a fourth power of length, converting cm⁴ to mm⁴ requires multiplying by 10,000. Each implemented formula should be tested with known examples, limiting cases, and invalid inputs.
Composite and custom sections need additional checks for centroid location, axis selection, holes, geometry validity, and numerical stability before they are suitable for use.