# Mass Moment of Inertia Calculator

The mass moment of inertia calculator is a complex tool that helps estimate the moment of inertia of objects with different shapes. This physical quantity is otherwise known as the angular mass or rotational inertia. The moment of inertia is a characteristic property of a rigid body. It plays a similar role in the dynamics of **rotational motion** as the normal mass in the dynamics of **translational motion**. For example, the mass in the kinetic energy equation is replaced by the moment of inertia in the rotational energy equation.

You can use the mass moment of inertia calculator right now - **just select a figure and enter its parameters**. Or read on to learn what is the moment of inertia, what are its units, and how to calculate the moment of inertia. In the following text, we have also prepared a moment of inertia table with about **23 different figures**. It contains almost all of the most common object shapes.

## What is the moment of inertia? - moment of inertia units

Moment of inertia is the measure of the body's rotational inertia relative to a defined, **fixed axis of rotation**. It determines the torque which is needed for a desired angular acceleration. It is just like how mass determines the force needed for a desired acceleration. In other words, **the moment of inertia tells us how difficult it is to put an object into rotation around a specific axis**. Remember that the choice of axis is very important, the final moment of inertia value might strongly depend on it!

The physical dimension of the moment of inertia is `mass * length²`

. The SI unit of the moment of inertia is kilogram meter squared `kg * m²`

and the imperial or US units is pound-foot second squared `lb * ft * s²`

or pound foot squared `lb * ft²`

. With the mass moment of inertia calculator, you can perform calculations in any of those units you prefer.

## Moment of inertia equation

The moment of inertia `I`

of a material point is the product of its mass `m`

and the square of the distance `r`

from the axis of rotation. It can be expressed with the following moment of inertia equation:

`I = m * r²`

If you consider a body consisting of `n`

material points, then the total moment of inertia is simply the sum of their moments of inertia:

`I = Σ(mi * ri²)`

where

`Σ`

is the symbol of the summation. It sums all components from`i = 1`

to`i = n`

,`mi`

is the mass of`i-th`

material point,`ri`

is the distance of`i-th`

material point from the axis of rotation.

However, for bodies with a constant distribution of mass, the summation in the above formula becomes an integral:

`I = ∫(r² * dm)`

where integration takes place over the entire volume `V`

of the body.

Although integration is not always an easy task, there are many **ready-made formulas** for the moment of inertia of specific solids. You can select the figure from the list in this mass moment of inertia calculator or check the moment of inertia table in the next section.

The mass moment of inertia of a body that we just described, and the second moment of area are often confused. Remember that the mass moment of inertia units are `kg * m²`

(`lb * ft * s²`

or `lb * ft²`

) and the second moment of area units are `m⁴`

(`ft⁴`

).

## Moment of inertia table

You have already learned what is the moment of inertia and how you can calculate it from its definition. In the table below, we have listed moment of inertia equations for simple objects with constant mass density, that can be selected in our mass moment of inertia calculator. When calculating moments of inertia, it is sometimes useful to exploit **the parallel axis and perpendicular axis theorems** to estimate moments of inertia about different axes.

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