How to use this calculator
- Enter the torque. Enter the tightening torque applied to the bolt or nut.
- Set the nut factor. Set K for the condition: ≈0.20 dry, 0.15 lubricated, 0.10 anti-seize.
- Enter the diameter and thread. Enter the nominal bolt diameter and thread pitch so tensile stress area can be estimated.
- Set proof and scatter. Enter proof strength, target proof-load percentage and a torque-control scatter band for the assembly method.
- Read the preload check. Read clamp force, low/high scatter estimates, proof-load utilization and the torque for your target preload.
How it works
The short-form torque–tension relation gives the clamp force a bolt develops from the tightening torque: F = T / (K · d) where T is the applied torque, d the nominal bolt diameter, and K the nut factor. K lumps the thread friction, under-head friction and thread lead into one empirical coefficient — it is not the coefficient of friction. Most of the torque never reaches the bolt as tension: typically only about 10–15% becomes preload, and the rest is spent overcoming friction under the head and in the threads. That is why K — and anything that changes friction, like plating or lubricant — dominates the result. The bolt preload guide covers the joint mechanics behind the target preload.
A torque number by itself is not enough to tell whether the joint is close to proof.
This calculator also estimates the thread tensile stress area,
A_t = (π / 4) · (d − 0.9382P)^2
then multiplies by proof strength:
F_p = S_p · A_t
The proof-load utilization is F / F_p, and the target torque is found
by putting the chosen target preload back into T = K · F · d. Use the
exact standard stress area and fastener proof strength when releasing a real joint.
| Question | Use this result | What it answers |
|---|---|---|
| What clamp force did this torque produce? | Preload (clamp force) | Calculated bolt tension from F = T/(K·d). |
| How far could torque scatter move it? | Preload low/high estimate | Entered scatter band around the calculated preload. |
| Is the bolt near proof load? | Proof-load utilization | Calculated preload divided by estimated proof load. |
| What torque targets 75% proof load? | Torque for target preload | Target preload from proof load, converted back to torque with the same K. |
This page solves preload from an applied torque. If you are starting from a desired clamp load, use the torque to tension calculator to solve the required torque; for common starting values by size and grade, use the bolt torque spec chart.
Bolt preload formula, equation and pretension wording
In most shop and design references, bolt preload,
bolt pretension and clamp force describe the same
tensile force locked into the fastener after tightening. The short-form
bolt preload formula is also written as the
bolt preload equation:
F = T / (K · d)
A bolt preload calculation or bolt pretension calculation
therefore needs three inputs: tightening torque T, nut factor
K and nominal bolt diameter d. Change any one of those
and the delivered preload changes immediately.
The focused bolt preload formula and
bolt preload calculation pages split out
the equation and worked examples for quick search paths. Related exact-intent
entries include M10 bolt preload,
bolt clamp force calculator,
torque-tension equation and
bolt pretension calculation.
Worked example
Verified against the live calculator
Tightening an M10 bolt (d = 10 mm) to 30 N·m dry, with K = 0.20:
F = 30 / (0.20 × 0.010) ≈ 15,000 N — about a 15 kN
clamp force. Lubricate the same bolt so K drops to 0.15 and the identical 30 N·m
now gives F = 30 / (0.15 × 0.010) ≈ 20,000 N, about 20 kN.
Same torque, a third more preload — which is exactly why lubricated bolts get a
lower torque spec. With an M10×1.5 class-8.8 screening setup
(S_p = 600 MPa), the stress area is about 58 mm²,
proof load is about 34.8 kN, and 15 kN is about
43% of proof load. A 75% proof-load target is about
26.1 kN, which takes roughly 52 N·m with
K = 0.20. With ±30% torque-control scatter, the 30 N·m preload
estimate spans about 10.5–19.5 kN.
Frequently asked questions
How do you calculate bolt preload from torque?
Preload F = T / (K · d), where T is the applied torque, K the nut factor, and d the nominal bolt diameter. For 30 N·m on an M10 (d = 0.010 m) with K = 0.20: F = 30 / (0.20 × 0.010) ≈ 15,000 N (15 kN).
What is the nut factor (K-factor)?
K is a single empirical coefficient that lumps the thread friction, under-head friction and thread geometry into one number, so torque and preload relate as T = K · F · d. It is roughly 0.20 dry/as-received, 0.15 lubricated, and 0.10 with anti-seize.
Why does lubrication change the torque?
Lubricant lowers the friction, which lowers K. Because F = T/(K·d), a lower K means the same torque produces more preload — so lubricated bolts must be tightened to a lower torque to avoid over-stretching. Going from K = 0.20 to 0.15 raises preload by about a third for the same torque.
How do I compare preload with bolt proof load?
Estimate tensile stress area from thread pitch, multiply by proof strength, then compare calculated preload with that proof load. This calculator reports proof-load utilization and the torque needed for a target percentage such as 75% of proof load.
Why is there a preload low and high estimate?
Torque control is approximate because friction dominates the tightening torque. The low and high results apply the entered torque scatter band around the calculated preload so you can see how far the delivered clamp force may move.
What torque for an M10 bolt?
It depends on the target preload and the nut factor, not just the size. As a worked figure, 30 N·m on an M10 with K = 0.20 (dry) gives about 15 kN of clamp force; set the torque to hit your target preload (typically 75–90% of proof load).
Is 75–90% of proof load the right target?
Yes — preloading to about 75–90% of the bolt’s proof load is the typical target for a reusable, properly designed joint. It keeps the joint clamped and the bolt in its elastic range; back off for soft or fatigue-sensitive joints.
Does this work in metric and imperial?
Yes — enter torque in N·m or lbf·ft and diameter in mm or inches; the preload is shown in N, kN, tonne and lbf.
Method & assumptions
- Short-form torque–tension F = T/(K·d) with a single lumped nut factor — it does not separate thread and under-head friction.
- K varies widely with finish, plating, coating and lubricant; the 0.20 / 0.15 / 0.10 values are typical, not exact — measure K if the joint matters.
- Torque control is only about ±25–35% accurate on the actual preload because friction scatters; use angle or stretch control where preload is critical.
- Tensile stress area uses the common 60° thread approximation; verify the exact standard stress area, proof strength, joint stiffness, embedment and fatigue for released designs.