Using nut factor K = 0.2 — Plain, unlubricated steel.
Results
Clamp force (preload)
25 kN
Installation torque
50 N·m
Tensile stress
431 MPa
% of proof load
71.8%
Proof load
34.8 kN
Factor of safety (proof)
1.39
Preload is within the bolt proof load with margin to spare.
More Information
How bolt torque and preload are related
When you tighten a bolt, most of the applied torque is consumed by friction under the head and in the threads; only a small fraction is converted into the axial clamp force (preload) that actually holds the joint together. The widely used short-form relationship captures this with a single nut factor K:
where T = tightening torque (N·m), K = nut factor (dimensionless), d = nominal thread diameter (m), and F = bolt preload / clamp force (N). Rearranged, the preload from a known torque is F = T / (K · d).
Preload stress and proof load
The preload creates tensile stress across the bolt's thread tensile stress area A_s:
The bolt's proof load is F_proof = A_s · S_proof, where S_proof is the property-class proof strength. A common assembly target is roughly 75% of proof load, which keeps the joint tight while leaving margin against yield. This calculator reports preload as a percentage of proof load and the factor of safety FoS = F_proof / F.
Worked example: M10 class 8.8, dry
For an M10 bolt (d = 0.010 m, A_s = 58 mm²) tightened to T = 50 N·m with a dry nut factor K = 0.20: preload F = 50 / (0.20 × 0.010) = 25 000 N = 25 kN. Tensile stress σ = 25 000 / 58 ≈ 431 MPa. The class 8.8 proof load is 58 × 600 = 34.8 kN, so the preload sits at about 72% of proof — a sensible target.
Frequently asked questions
What is the nut factor K?
K is an empirical torque coefficient that lumps together thread friction, under-head friction and thread geometry. Typical values range from about 0.12 (waxed/PTFE) to 0.22 (zinc plated, dry). It is not a fundamental constant — it should be validated for critical joints.
Why does lubrication reduce the required torque?
Lubrication lowers friction, so a smaller fraction of torque is lost and more goes into preload. The same torque on a lubricated bolt therefore produces a higher clamp force — which is why you should use the K value that matches the actual thread condition.
What preload should I aim for?
For general structural joints, 70–80% of proof load is a common target. Lower values may be used where fatigue, gasket seating or relaxation are concerns. Always follow the joint's design specification where one exists.
Limitations
- The short-form method does not separate thread and under-head friction or account for joint stiffness, embedment or relaxation.
- Nut factors are representative starting points; real K depends on plating batch, surface finish and lubricant.
- Results assume a ductile steel fastener in pure tension — not for safety-critical certification without verification.