Moment of Inertia Calculator

Compute area moment of inertia for common shapes.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

Compute area moment of inertia for common shapes.

It combines Shape, Width (Rectangle), Height (Rectangle), Radius (Circle) to estimate Moment of Inertia, Shape.

Formula & Method

Area moment of inertia formulas: rectangle

I=\frac{bh^3}{12}

and circle

I=\frac{\pi r^4}{4}

Notation used in the formulas: $R$ = Moment of Inertia; $x_{1}$ = Shape; $x_{2}$ = Width (Rectangle); $x_{3}$ = Height (Rectangle); $x_{4}$ = Radius (Circle).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Reference Book

Engineering Mechanics: Statics & Dynamics

Russell C. Hibbeler · Pearson

A standard mechanics reference for torque, pulleys, equilibrium, load balance, and rigid-body reasoning.

View Book

Inputs Used

Shape: Used directly in the calculation.
Width (Rectangle): Used directly in the calculation.
Height (Rectangle): Used directly in the calculation.
Radius (Circle): Used directly in the calculation.

Related Calculators

Gear Ratio Calculator - Calculate gear ratio, speed ratio, and torque multiplier.
Torque Calculator - Calculate torque from force and lever arm distance.
Pulley System Calculator - Estimate mechanical advantage and effort for a pulley system.
Spring Constant Calculator - Calculate spring constant using Hooke's law.
Thermal Expansion Calculator - Calculate length change from thermal expansion.
Heat Transfer Calculator - Calculate heat energy using Q = m · c · ΔT.
Pressure Calculator - Calculate pressure from force and area.
Flow Rate Calculator - Calculate volumetric flow from pipe diameter and velocity.