Section modulus converter
Convert the elastic or plastic section modulus of a beam between in³, cm³ and mm³, as US and European steel tables give it.
That's 3.3× as strong in bending as a 2×4 stud on edge, while an IPE 300 steel beam is 3.4× stronger in bending. In S235 steel it reaches yield at about 38.51 kN·m of bending.
What it means
How strong is that beam?
The moment uses a stress of 235 MPa, the yield of S235 steel (A36 is 250 MPa), with no safety factor. Design to your code.
Every unit
That section in every unit
Learn
Three things worth knowing
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in³ × 16.39 = cm³
One cubic inch is 16.387 cm³, so a W8×10 at 7.81 in³ is about 128 cm³.
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Galileo’s beam
Galileo studied the strength of beams in 1638; Navier gave the bending formula σ = M y / I in 1826, and S = I / y gathers the shape into one number.
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Not the moment of inertia
Section modulus (in³, cm³) is for strength; the moment of inertia (in⁴, cm⁴) is for stiffness and deflection. They are easy to swap in a table.
Shortcuts
Popular section conversions
Background
About section modulus
A beam’s section modulus S links the bending moment it carries to the stress in its outer fibres: σ = M ÷ S. It depends only on the shape: for a rectangle b wide and h deep, S = b h² ÷ 6, which is why a joist on edge is so much stronger than flat.
US tables list S in in³, European ones in cm³ (Wel); the plastic modulus (Z or Wpl) uses the same units.