How Bolt Torque Is Calculated
Why torque is a proxy for preload, the nut factor K, and how to compute the torque for a given clamping force.
Why torque is a proxy, not the real target
When tightening a bolt, the real quantity we want is a specific preload — how tightly the bolt clamps the joined parts together. But measuring that force directly is difficult in practice, so engineers use an easier-to-measure value instead: torque. The relationship between the two is given by:
T = K × D × F
T — applied torque (N·m), K — the nut factor (dimensionless, represents friction), D — nominal bolt diameter (m), F — target preload force (N).
Why the K factor is not a single number
K is effectively a combined indicator of thread friction and the friction under the bolt head / nut face. It varies widely with surface condition:
| Condition | Typical K |
|---|---|
| Dry, unfinished steel | ~0.20 |
| Lightly oiled steel | ~0.17 |
| Zinc-plated | ~0.18–0.20 |
| Molybdenum disulfide (MoS₂) grease | ~0.12–0.14 |
These are typical ranges; in a real application you must always use the K value from your bolt/coating manufacturer — that is why torque tables published by different sources can disagree. It is normal and comes from differences in the assumed friction.
How the target preload is chosen
It is usually chosen as a percentage of the bolt's proof load (a reference load near the yield/strength limit) — about 75% of proof load for joints that will be disassembled and reassembled, up to ~90% for permanent joints.
Worked example — M10, grade 8.8, dry steel
Tensile stress area (standard M10, As): 58.0 mm². Grade 8.8 proof stress: ≈ 660 MPa. Proof load = 58 × 660 = 38,280 N. Target preload (75% of proof) = 28,710 N. T = 0.20 × 0.010 × 28,710 ≈ 57.4 N·m.