How this calculation works
An applied torque does not uniquely determine bolt preload. Friction represented by the empirical nut factor and variation in delivered torque both affect the initial tension. This page calculates the corner values of an entered uncertainty interval.
Fmin = T(1 − tolerance)/(Khigh d); Fmax = T(1 + tolerance)/(Klow d)A worked example
For 40 N m, a 10 mm bolt, ±10 percent torque and K from 0.15 to 0.25, the low estimate is 14400 N and the high estimate is 29333.33 N. Dividing the high force by 58 mm² gives 505.747 MPa nominal tension.
Good to know
No proof-strength verification, joint stiffness, separation, slip, fatigue or long-term relaxation is included. Actual torque-preload behavior needs suitable test data and the relevant fastener procedure. The example K range is illustrative rather than a material specification.
Reference: NASA — preload and torque-control variation (opens in a new tab) ↗
What this model answers
An applied torque does not uniquely determine bolt preload.
Friction represented by the empirical nut factor and variation in delivered torque both affect the initial tension. This page calculates the corner values of an entered uncertainty interval.
The Fully restrained bar thermal stress and force calculator estimates an elastic axial stress from a known strain constraint. Torque-derived preload instead uses an empirical nut factor and cannot be substituted for measured strain.
Keep the input conventions consistent
The torque must be effective tightening torque for this model; prevailing or running torque is not automatically removed.
Use nominal diameter for the KFd relation and a separately entered tensile stress area for nominal stress. The nut factor is not identical to a friction coefficient.
Read the result carefully
The smallest preload combines low torque with the largest nut factor.
The largest combines high torque with the smallest factor. These deterministic extremes are not statistical confidence limits and do not supply a recommended tightening torque.
The same nominal tightening torque can correspond to a range of preload when the nut factor is uncertain. Compare the low and high assumptions rather than reporting their midpoint as a measured clamp force. Thread condition and lubrication belong in the source of that uncertainty, not in an unexplained precision claim.
Work through the numbers
For 40 N m, a 10 mm bolt, ±10 percent torque and K from 0.15 to 0.25, the low estimate is 14400 N and the high estimate is 29333.33 N.
Dividing the high force by 58 mm² gives 505.747 MPa nominal tension.
Where the calculation stops
No proof-strength verification, joint stiffness, separation, slip, fatigue or long-term relaxation is included.
Actual torque-preload behavior needs suitable test data and the relevant fastener procedure. The example K range is illustrative rather than a material specification.
A few questions, answered
Does a lower nut factor mean lower preload?
At fixed torque and diameter it means higher estimated preload because F = T/(Kd).
What should I change in the comparison?
Remove torque tolerance while retaining nut-factor variation; a preload range still remains.