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Moments of Inertia of Common Shapes

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rectangle x' = 1 12 bh3 y' = 1 12 b3h Ix = 1 3 bh3 Iy = 1 3 b3h JC = 1 12 bh(b2 + h2)
triangle x' = 1 36 bh3 y' = 1 12 bh3
circle x = y = 1 4 πr4 JO = 1 2 πr4
semicircle Ix = Iy = 1 8 πr2 JO = 1 4 πr4
quarter circle Ix = Iy = 1 16 πr4 JO = Iz = 1 8 πr4
ellipse x = 1 4 πab3 y = 1 4 πa3b JO = 1 4 πab(a2 + b2)