Free · Algebra and geometric relations

Centroidal Second Moments of Plane Sections

Find area second moments about horizontal and vertical centroidal axes for six planar sections.

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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For the worked example, I==x== = 16, I==y== = 9.

Rectangle Ix=bh³/12 and Iy=b³h/12; circle Ix=Iy=πr⁴/4

Enter these known values and leave the other values blank.

These are geometric area moments in length to the fourth power, not mass moments.
Axes pass through the centroid. For the triangle, a is horizontal apex offset from the left base endpoint; b is full base width.
Ellipse a is vertical semiaxis and b is horizontal semiaxis. A semicircle uses the centroidal horizontal axis and vertical symmetry axis.

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture.