# Moment of Inertia of a Rectangle

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

### rectangle, Solid Plane, z Axis formula

$$\large{ I_z = \frac {1}{12}\; m \; \left( l^2 + w^2 \right) }$$

$$\large{ I_z = \frac {1}{12} \;l\;w \; \left( l^2 + w^2 \right) }$$

$$\large{ I_{z1} = \frac {1}{12}\;m \; \left( 4\;l^2 + w^2 \right) }$$

### rectangle, Solid Plane, x Axis formula

$$\large{ I_x = \frac {1}{12}\; l\;w^3 }$$

$$\large{ I_x = \frac {1}{12}\; m \; l^2 }$$

$$\large{ I_{x1} = \frac {1}{3}\; l\;w^3 }$$

$$\large{ I_{x1} = \frac {1}{3}\; m \; w^2 }$$

### rectangle, Solid Plane, y Axis formula

$$\large{ I_y = \frac {1}{12}\; l^3\;w }$$

$$\large{ I_{y1} = \frac {1}{3}\; l^3\;w }$$

### rectangle, Hollow Core Plane, x Axis formula

$$\large{ I_x = \frac {l\;w^3}{12} - \frac {l_1\;w_1{^3} }{12} }$$

### rectangle, Hollow Core Plane, Y Axis formula

$$\large{ I_y = \frac {l^3\;w}{12} - \frac {l_1{^3} w_1}{12} }$$

Where:

$$\large{ I }$$ = moment of inertia

$$\large{ l }$$ = length

$$\large{ l_1 }$$ = length

$$\large{ m }$$ = mass

$$\large{ w }$$ = width

$$\large{ w_1 }$$ = width