Threads remove material, so a bolt fails through its threaded region at an effective area smaller than the shank but larger than the bare minor-diameter circle, because the thread root supports some load. That effective area is the tensile stress area: At = π/4 (D − 0.9743/n)² for Unified inch threads (the ASME B1.1 form, with n threads per inch) and π/4 (d − 0.9382·P)² for ISO metric (the ISO 898-1 §9.1.6.1 form). Both evaluate a diameter between the pitch and minor diameters, and both correlate with measured tensile strength — a 1/2-13 UNC comes to the published 0.1419 in², an M16 × 2.0 to 156.7 mm².
Almost every fastener-strength number is this area times a material stress. Proof load is At × proof strength; the 75%-of-proof preload target, the bolt tensile stress σ = F/At, and the H28 bolt-break-before-strip engagement criterion (LE = 2·At over the thread shear area per unit length) all start from it. The formula also makes one design effect visible: a fine-pitch thread removes less material, leaving a larger At — a measurably stronger bolt from the same blank diameter.