Moment of Inertia Calculator
Calculate centroid coordinates (x̄, ȳ), second moment of area (Ix, Iy), elastic section modulus, and radius of gyration for rectangular, circular, I-beam, and composite cross-sections.
I_xx = ∫ y² dA = I_c + A·d²
Beam Master handles any combination of point loads, uniform distributed loads (UDL), varying loads (UVL), and applied moments with instant SFD, BMD, and deflection curves.
How to Calculate Composite Cross-Section Inertia
For built-up shapes (I-beams, T-sections, channels), follow this 3-step engineering process:
Find Centroid (ȳ)
ȳ = (∑ A_i · y_i) / (∑ A_i)
Individual I_i
I_i = (b_i · h_i³) / 12
Parallel Axis
I_total = ∑ (I_i + A_i · d_i²)
Engineering Formulas & Governing Equations
Rectangle Centroidal Moment of Inertia
Equation 01Second moment of area for a solid rectangular section of base b and height h about its neutral centroidal axes.
Parallel Axis Theorem (Steiner’s Theorem)
Equation 02Calculates the moment of inertia of compound sections about the global neutral axis shifted by distance d.
Solid Circular Cross-Section
Equation 03Second moment of area for a solid circle with diameter d and radius r.
Elastic Section Modulus (S or Z)
Equation 04Measures bending resistance against peak fiber flexural stress: σ_max = M / S_x.
Calculation Details & Clarifications
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