Bolt Torque from Preload

The engineering

The K-factor buries all the ugly physics — thread friction, underhead friction, thread geometry — into one empirical number. Dry steel runs K ≈ 0.2, lubricated ≈ 0.15, moly or wax-plated can hit 0.10. That spread is the number that bites: the same 40 N·m puts twice the preload into a waxed bolt as a dry rusty one, which is how 'torqued to spec' joints still fail.

Torque is a proxy, not the quantity you care about — preload is. Only about 10–15% of the applied torque actually stretches the bolt; the rest is spent on friction. When preload really matters (head bolts, flight hardware), people measure stretch or turn-of-nut instead of trusting the wrench.

Where this math comes from

Threaded fasteners are Renaissance technology, but controlled tightening is a twentieth-century idea. Conrad Bahr, working for the New York City water department, claimed the first torque wrench in 1918 after watching flange bolts tightened by feel leak anyway. The K-factor shorthand grew out of postwar automotive and aerospace bolting studies that needed one dial-in number instead of a friction-coefficient research project per joint.

N. Motosh's 1976 analysis put the full long-form torque equation (thread pitch, friction angles, bearing radius) on rigorous footing, and Germany's VDI 2230 guideline turned bolted-joint design into an engineering discipline of its own. The single-K shortcut survives because it is honest about its own imprecision.

1. 1918Conrad BahrTorque wrench invented for NYC water-main flange bolts.
2. 1976N. MotoshRigorous long-form bolt torque–preload equation published.
3. 1977VDI (circa)VDI 2230 systematizes bolted-joint calculation.

See the full timeline of the math behind every calculator →

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