List of area moments of inertia: Wikis

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The following is list of area moments of inertia. The area moment of inertia or second moment of area has a unit of dimension length⁴, and should not be confused with the mass moment of inertia. Each is with respect to a horizontal axis through the centroid of the given shape, unless otherwise specified.

Description	Area moment of inertia	Comment	Reference
a filled circular area of radius r	$I_0 = \frac{\pi r^4}{4}$		^[1]
an annulus of inner radius r₁ and outer radius r₂	$I_0 = \frac{\pi}{4} \left({r_2}^4-{r_1}^4\right)$	For thin tubes, this is approximately equal to: $\pi \left(\frac{{r_2}+{r_1}}{2}\right)^3 \left({r_2}-{r_1}\right)$ or $π$ times the cube of the average radius times the thickness.
a filled circular sector of angle θ in radians and radius r with respect to an axis through the centroid of the sector and the centre of the circle	$I_0 = \left(\theta -\sin\theta\right)\frac{r^4}{8}$
a filled semicircle with radius r with respect to a horizontal line passing through the centroid of the area	$I_0 = \left(\frac{\pi}{8} - \frac{8}{9\pi}\right)r^4$		^[2]
a filled semicircle as above but with respect to an axis collinear with the base	$I = \frac{\pi r^4}{8}$	This is a consequence of the parallel axis theorem and the fact that the distance between these two axes is $\frac{4r}{3\pi}$	^[2]
a filled semicircle as above but with respect to a vertical axis through the centroid	$I_0 = \frac{\pi r^4}{8}$		^[2]
a filled quarter circle with radius r entirely in the 1st quadrant of the Cartesian coordinate system	$I = \frac{\pi r^4}{16}$		^[3]
a filled quarter circle as above but with respect to a horizontal or vertical axis through the centroid	$I_0 = \left(\frac{\pi}{16}-\frac{4}{9\pi}\right)r^4$	This is a consequence of the parallel axis theorem and the fact that the distance between these two axes is $\frac{4r}{3\pi}$	^[3]
a filled ellipse whose radius along the x-axis is a and whose radius along the y-axis is b	$I_0 = \frac{\pi}{4} ab^3$
a filled rectangular area with a base width of b and height h	$I_0 = \frac{bh^3}{12}$		^[4]
a filled rectangular area as above but with respect to an axis collinear with the base	$I = \frac{bh^3}{3}$	This is a trivial result from the parallel axis theorem	^[4]
a filled triangular area with a base width of b and height h with respect to an axis through the centroid	$I_0 = \frac{bh^3}{36}$		^[5]
a filled triangular area as above but with respect to an axis collinear with the base	$I = \frac{bh^3}{12}$	This is a consequence of the parallel axis theorem	^[5]
a filled regular hexagon with a side length of a	$I_0 = \frac{5\sqrt{3}}{16}a^4$	The result is valid for both a horizontal and a vertical axis through the centroid.