# List of moments of inertia

The following is a list of moments of inertia.

Table of contents |

2 Mass moments of inertia |

## Area moments of inertia

Area moments of inertia have units of dimension length^{4}. Each is with respect to a horizontal axis through the centroid of the given shape, unless otherwise specified.

### Circles and related areas

For a filled circular area of radius , .

For a filled semicircle with radius resting atop the -axis, .

For a filled quarter circle with radius entirely in the upper-right quadrant of the Cartesian plane, .

For an ellipse whose radius along the -axis is and whose radius along the -axis is , .

### Rectangle

For a filled rectangular area with a base width of and height , .

For an axis collinear with the base, . (This is a trivial result from the parallel axis theorem.)

### Triangle

For a filled triangular area with a base width of and height , .

For an axis collinear with the base, . (This is a consequence of the parallel axis theorem and the fact that the distance between these two axes is always .)

## Mass moments of inertia

Mass moments of inertia have units of dimension mass × length^{2}.

Description | Figure | Moment(s) of inertia | Comment |
---|---|---|---|

Thin cylindrical shell with open ends, of radius and mass | — | ||

Thick cylinder with open ends, of inner radius , outer radius and mass | — | ||

Solid cylinder of radius , height and mass | — | ||

Thin disk of radius and mass | — | ||

Solid sphere of radius and mass | — | ||

Hollow sphere of radius and mass | — | ||

Right circular cone with radius , and mass | — | ||

Solid rectangular prism of height , width , and depth , and mass | For a similarly oriented cube with sides of length and mass , . | ||

Rod of length and mass | This expression is an approximation, and assumes that the mass of the rod is distributed in the form of an infinitely thin (but rigid) wire. | ||

Rod of length and mass | This expression is an approximation, and assumes that the mass of the rod is distributed in the form of an infinitely thin (but rigid) wire. |