theorems
Principal Moment of Inertia Calculator
Calculate principal area moments from planar section properties.
Principal Moment of Inertia Calculator
Define your section
Principal moments
Moment of inertia about the x-axis
Moment of inertia about the y-axis
Signed product of inertia
Calculated properties
I₁,₂ = (Ix + Iy)/2 ± √[((Ix − Iy)/2)² + Ixy²]- Enter Ix, Iy and Ixy in the selected unit⁴. The sign convention for Ixy affects the reported angle.
Length inputs are converted to millimetres for calculations. Review the assumptions before using results in engineering work.
About this calculation
Enter the required dimensions and select the appropriate length unit. The calculator displays results based on the selected calculation and its stated assumptions.
Moment of inertia and related section properties depend on the geometry, reference axes, units, and assumptions used. Review the displayed formula and assumptions before using any result.
These tools are intended for educational and preliminary engineering calculations. Independently verify critical results before using them in engineering design or safety-related work.
Calculation methodology
Learn about formulas, units, assumptions, and calculation limitations in our calculation methodology.