Moment of inertia of a triangle from three points
Enter the three vertices — the calculation uses the general polygon formula, so the orientation of the sides does not matter.
Formulas
About this calculator
For an arbitrary triangle it is easier to work from vertex coordinates than from legs: the area comes from the shoelace formula and the moments from its second-moment generalisation, after which the axes are moved to the centroid. The same algorithm extends to any polygon, and it is what the main calculator runs on.
Frequently asked questions
Compute the area and centroid with the shoelace formula, then the second moments about the original axes, and finally transfer them to the centroid by subtracting A·d².
No. The sign of the area flips, but its magnitude and every derived property stay the same.