Thread engagement length answers the question every tapped hole poses: how many threads does a steel bolt need in a housing before the bolt breaks instead of the threads stripping? The FED-STD-H28/2B criterion for equal-strength materials is LE = 2·At divided by the external thread’s shear area per unit length — at that depth the thread shear capacity (at roughly half the tensile strength in shear) equals the bolt’s breaking load. For standard coarse threads that works out to roughly 0.6–0.9 times the nominal diameter; a 1/2-13 needs 0.289 in, about 3.8 threads.
The stripping direction of failure is the one to design out, because a broken bolt announces itself and is replaceable, while stripped internal threads fail progressively, can pass inspection torque, and ruin the tapped part. When the tapped material is weaker than the bolt — the usual reason the question matters — the H28 J factor scales the requirement: J = (external shear area × bolt strength) ÷ (internal shear area × tapped-material strength), and J > 1 multiplies the required depth, commonly reaching 1.5–2 diameters in aluminum and more in plastics, which is why soft housings get threaded inserts or deeper bosses. Standard nuts never need this analysis: their heights (≈0.8–0.9 × d) are proportioned with their property class so the bolt breaks first.
Engagement length is also the right lever when a tapped joint in soft material needs more strength — the tap drill guidance is to add depth of engagement, not thread percentage, since pushing past 75% thread engagement adds little strength while multiplying tap-breakage risk.