Bolt Preload Formula
The common bolt preload formula is the short-form torque-tension relation. It estimates clamp force from tightening torque, nut factor and nominal bolt diameter, then the calculator can compare that preload with proof load.
bolt preload formula bolt preload equation torque tension formula
The equation
The short-form relation is T = K * d * F. Rearranged to solve clamp force:
F = T / (K * d)
Proof-load check
The live calculator also estimates tensile stress area from thread pitch, proof load from proof strength, and the torque needed for a target percentage of proof load.
Typical nut factor values
- Dry/as-received: K near 0.20 is a common estimate.
- Lightly lubricated: K near 0.15 is a common estimate.
- Anti-seize/coatings: K can be lower and must match the assembly condition.
Worked example
Tighten an M10 bolt to 30 N*m with K = 0.20. F = 30 / (0.20 * 0.010) = 15,000 N, or 15 kN.
Frequently asked questions
Is nut factor K the same as friction coefficient?
No. Nut factor is a lumped empirical factor that includes thread friction, under-head friction and thread geometry.
Related pages
- Bolt preload torque calculator - calculate clamp force, proof-load utilization and preload scatter.
- Bolt preload formula - equation and nut-factor definitions.
- Bolt preload explained - joint mechanics, proof load targets and preload scatter.
- Bolt torque spec chart - starting torque values by size and grade.