Moment of Inertia Calculator
Compute the moment of inertia of standard rigid bodies — spheres, disks, hoops, rods, and point masses — from their mass and characteristic size.
Shape
kg
m
Resistance to angular acceleration about the chosen axis
- 1
r²
0.5 × 0.5 = 0.25 m² - 2
m × r²
2 kg × 0.25 m² = 0.5 kg·m² - 3
I = k × m × r²
0.4 × 0.5 = 0.2000Shape factor k = 0.4 for solid sphere (about diameter).
How does this calculator work?
Moment of inertia equals a shape factor times mass times size squared (I = k·m·d²). A solid sphere uses k = 2/5, a disk 1/2, a hoop 1, and a rod 1/12 about its center. Enter the mass and the radius or length, pick the shape, and read I in kg·m².
Formula
How this is calculated
Moment of inertia I measures how strongly a body resists angular acceleration about a given axis, playing the rotational role that mass plays in linear motion. Every standard shape shares the form I = k·m·d², where m is the mass in kilograms, d is the characteristic size in meters (radius r for round bodies, length L for rods), and k is a dimensionless geometric factor set by the shape and the location of the rotation axis.
Select a shape to pick the correct factor k: solid sphere about a diameter uses 2/5, a thin hollow sphere uses 2/3, a solid disk or cylinder about its central axis uses 1/2, a hoop or thin-walled cylinder uses 1, a uniform rod rotated about its center uses 1/12, the same rod about one end uses 1/3, and a point mass at distance r uses 1. The calculator multiplies k by m and by the square of the size to return I in kg·m².
These formulas assume uniform density, ideal geometry, and rotation about the stated axis. Doubling the size quadruples the inertia because of the square term, while inertia scales linearly with mass. For composite bodies, sum the contributions of each part and apply the parallel-axis theorem (I = I_cm + m·d²) when shifting the axis away from the center of mass.
Frequently asked questions
In a hollow sphere all the mass sits at the outer radius, so it has a larger factor (2/3 versus 2/5). Mass farther from the axis contributes more to inertia because of the r² dependence.
For the rod options the characteristic size is the full length L of the rod. For spheres, disks, hoops, and a point mass, the size field is the radius r (the distance from the axis).
Use the parallel-axis theorem: I = I_cm + m·d², where I_cm is the central moment of inertia and d is the distance between the two parallel axes.
Also known as
TG we-Calculate Editorial Team. (2026). Moment of Inertia Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/moment-of-inertia-calculator
TG we-Calculate Editorial Team. "Moment of Inertia Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/moment-of-inertia-calculator.
TG we-Calculate Editorial Team, "Moment of Inertia Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/moment-of-inertia-calculator
@misc{wecalculate_moment_of_inertia_calculator, title = {Moment of Inertia Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/moment-of-inertia-calculator}}, year = {2026}, note = {TG we-Calculate} }
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