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Section Calculator

Moment of Inertia Calculator

Instantly calculate Ixx, Iyy, section modulus, and radius of gyration for 7 cross-section shapes. Parallel axis theorem included. Covers area moment (beams) and mass moment (rotating bodies).

Cross-Section Shape
Parallel Axis Offset d 0.0 mm
Distance from centroid (parallel axis theorem)
Ixx [mm⁴]
Iyy [mm⁴]
Area A [mm²]
Centroid y_c [mm]
Section Mod. Wxx [mm³]
PropertyCentroidal AxisParallel Axis (I+Ad²)Unit

Theory

Rectangle: $I_{xx} = \dfrac{bh^3}{12}$,   $I_{yy} = \dfrac{hb^3}{12}$

Circle: $I = \dfrac{\pi d^4}{64}$,   Hollow: $I = \dfrac{\pi(d_o^4 - d_i^4)}{64}$

Parallel axis theorem: $I = I_c + Ad^2$

Section modulus: $W_{xx} = \dfrac{I_{xx}}{y_{max}}$,   Radius of gyration: $k = \sqrt{\dfrac{I}{A}}$

Engineering applications: FEM beam element section properties (BEAM188/BEAM189) · bending stress verification σ = M/W · flywheel and rotating disk mass moment of inertia · ANSYS Mechanical cross-section property input.