Section modulus formula
Section modulus is the single number that tells you how strong a cross-section is in bending. It combines the shape and size of a beam so that bending stress is simply the moment divided by the section modulus.
Variables
| S | Section modulus | in³ or m³ |
| I | Area moment of inertia | in⁴ or m⁴ |
| c | Distance to extreme fiber | in or m |
Rearranged
I = S × c
Worked example
A solid rectangular beam is 50 mm wide and 100 mm deep.
Use S = b h² / 6: 50 × 100² / 6 = 83,333 mm³.
A larger section modulus means a stronger beam in bending, because bending stress equals moment over S. For a rectangle it is b times h squared over six, so depth matters far more than width: doubling the depth roughly quadruples the strength.
Comparing real beam sections?
See the Steel Beam Properties Chart for tabulated section modulus values.
Section modulus and bending strength
Because bending stress is moment divided by section modulus, sizing a beam is a matter of finding a section whose S keeps the stress under the allowable limit. This is why beam tables list S for every size: pick the moment your beam must carry, divide by the allowable stress, and choose a section with at least that section modulus.
Why depth dominates
For a rectangle the section modulus grows with the square of the depth but only linearly with width. Turning a plank on edge, so its tall dimension resists the bending, makes it far stiffer and stronger than laying it flat. The same principle is why steel beams are deep and narrow rather than square.
FAQ
What is the section modulus formula?
Section modulus equals the area moment of inertia divided by the distance to the outer fiber, S = I / c. For a rectangle it is b h squared over 6.
How does section modulus relate to strength?
Bending stress equals the moment divided by the section modulus, so a larger S means lower stress and a stronger beam for the same load.
Why is a beam stronger on edge?
Section modulus depends on the square of the depth, so orienting a section so its tall side resists bending sharply increases strength.