Section modulus tells you how efficiently a beam's cross-section resists bending, independent of the material it's made from. Engineers and hobbyist builders alike use it to compare cross-section shapes and to check whether a beam under a known load will stay within a safe bending-stress limit.
How the Section Modulus Calculator works
The calculator first computes the moment of inertia (I) for the selected shape about its centroidal (neutral) axis, then divides by c — the distance from that axis to the extreme fiber — to get the section modulus, S = I/c. Rectangle and solid-circle formulas are exact closed forms (bh²/6 and πd³/32 respectively). The hollow circle subtracts the inner circle's moment of inertia from the outer circle's before dividing by c. The I-beam treats the section as a full B×H rectangle with two side rectangles removed to leave the web and flanges, ignoring the small fillets real rolled sections have at the web-flange junction — a standard simplification that stays accurate to within a percent or two for typical proportions.
Inputs and what they mean
All dimensions are entered in millimetres, matching common structural drafting practice. Section modulus (S) comes out in mm³ and moment of inertia (I) in mm⁴ — both large numbers for realistic beam sizes, which is expected. The optional bending moment is entered in kilonewton-metres (kN·m), a standard structural-engineering unit, and the resulting bending stress is reported in megapascals (MPa = N/mm²) so it can be compared directly against a material's published yield strength. Height is the input with the biggest effect on both I and S for rectangular and I-beam sections, since it enters the formulas raised to the second or third power — small increases in height produce outsized gains in bending resistance.
Limits and edge cases
This calculator handles pure elastic bending about the horizontal centroidal axis only — it does not account for lateral-torsional buckling, shear stress, combined axial-and-bending loading, or unsymmetrical bending about a skewed axis. The I-beam formula ignores fillet radii and assumes a doubly-symmetric section (equal top and bottom flanges), so it will not exactly match every manufacturer's published catalog value for a specific rolled shape — use it for estimating and comparing custom or built-up sections, and cross-check against a steel manufacturer's tables for a specific standard profile. For any load-bearing design, verify results against your local structural code and, where required, have a licensed engineer review the calculation.