Second Moment Of Area Formula

The property of a two dimensional plane which categorizes its deflection during loading is the second moment of area formula. The second moment of inertia rectangle is the product of height and cube of width divided by 12. The area moment of inertia of triangle is the product of width and cube of the height divided by 36. The formula to find second moment of inertia circle and semicircle is provided in the area moment of inertia formula.

Area Moment Of Inertia Formula

Area Moment of Inertia Formula:

Ix = w × h3 / 12
Iy = h × w3 / 12

Ix = w × h3 / 36

Ix, Iy = π × r4 / 8

Ix, Iy = π × r4 / 4


Ix, Iy = Area Moment Of Inertia
w = Width
h = Height
r = Radius

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The second area moment is used in mechanical design and can be found using the area moment of inertia formula. The second moment of area formula is provided for different shapes like rectangle, triangle, circle and semicircle.

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