The spare fifty percent
The elastic section modulus answers one question: at what moment does the OUTERMOST fibre reach yield. That is first yield, and it is not collapse. Push further and the yielded zone spreads inward from both faces until every fibre in the section is at . The section property that describes THAT state is the plastic section modulus , where is the width and the depth in the plane of bending, both in mm, and comes out in mm³.
The depth is the one that gets squared, in both formulas — which is the whole reason a joist stands on edge and not on its side. And compare the pair: exactly, for any rectangle. That fifty percent is the section's shape factor, the reserve capacity sitting past first yield that elastic design simply leaves on the table.
Turn the geometry into a capacity with — M-p equals Z f-y — where is the steel's yield strength in MPa and is the full plastic moment, the moment at which the section forms a hinge. Watch the arithmetic on the way out: mm³ × MPa gives N·mm, and a kN·m is a million of those. Answers that land a thousand or a million out are almost always this bridge, not the physics.