Bending stress is largest at the fibre furthest from the neutral axis, so in practice that is the only fibre anybody checks. Combine the section's stiffness with the distance to that worst fibre once, and you never have to carry them separately again. That combination is the elastic section modulus: $S = \dfrac{I}{c}$ — read aloud S equals I over c.

$I$ is the second moment of area in mm⁴. $c$ is the distance from the neutral axis to the extreme fibre, in mm — and on a symmetric section the neutral axis sits at mid-depth, so $c$ is HALF the depth, never the depth. $S$ comes out in mm³. That is the single most common slip in this chapter, and it is worth a factor of two in every stress you report afterwards.

Push the units through and the definition defends itself: mm⁴ divided by mm leaves mm³. Units guide, they do not confess — if a rearrangement will not cancel down to mm³ it is wrong and there is no appeal, but units that do work out never prove you right. The check runs one way only.

For a rectangle the algebra collapses to something worth memorising: $S = \dfrac{bh^{3}/12}{h/2} = \dfrac{bh^{2}}{6}$. Note what happened to the power — $I$ went as $h^{3}$, $S$ goes as $h^{2}$. Depth still beats width handsomely, just not quite as handsomely. This is the number steel handbooks print in their widest column, because it is the number a designer actually shops with.