What this calculator does
A bolted joint is held together by preload, not by torque. Torque is only the thing you can measure with a wrench, and it is a poor proxy: most of it is spent overcoming friction and never becomes clamp force at all. This calculator does the conversion in both directions that engineers actually need — from a target preload expressed as a percentage of the fastener’s proof load, to the tightening torque you would set on the tool — and it does it two ways so you can see how much the answer depends on assumptions you cannot measure on site.
It also reports what the bolt is really experiencing while the spanner is still on it: tension plus torsion, combined by von Mises. That number is usually a lot closer to the proof strength than the headline “75% of proof” suggests.
The formula
Short form. One lumped coefficient, the nut factor K:
T = K · F · d
T tightening torque (N·m), F preload (N), d nominal thread diameter (m), K dimensionless. K is measured, not derived — it is whatever a test rig said for that fastener, that coating, that lubricant and that joint face.
Long form. The same torque, decomposed into the three jobs it does:
T = F · [ P/(2π) + μ_t · d₂ / (2 cos β) + μ_b · d_n / 2 ]
└ pitch ┘ └── thread friction ─┘ └ head friction ┘
P thread pitch, d₂ thread pitch diameter, β half thread angle (30° for ISO metric and Unified, 14.5° for Acme), d_n effective bearing diameter under the turned head or nut — the mean of the bearing face OD and the hole, μ_t thread friction coefficient, μ_b under-head friction coefficient. All lengths in the same unit.
The first term is the only one doing useful work: P/(2π) is the ramp of the helix, the torque that actually stretches the bolt. The second is friction on the thread flanks, inflated by 1/cos β because a vee thread wedges — the normal force on the flank is larger than the axial force, so its friction is larger too. The third is friction under the head. In a typical dry steel joint the split is roughly 10% useful, 40% thread friction, 50% head friction.
Preload target. Proof load is F_proof = S_p · A_s, and the target is a stated fraction of it. Stress area A_s, pitch diameter d₂ and proof stress S_p are properties of the thread and property-class standards — you enter them from whichever standard governs your fastener (ISO 898-1 and ISO 724 for metric, SAE J429 or ASTM F3125 for inch). This tool deliberately ships no thread table and claims compliance with no standard.
Combined stress. While you are turning the fastener, the thread torque is reacted as torsion in the shank:
σ = F / A_s τ = M_thread / W_p W_p = π d_s³ / 16
d_s = √(4 A_s / π) σ_v = √(σ² + 3τ²)
Reading the result
Compare the two torque figures. They will not agree, and the gap is the whole story: the short form and the long form encode two different guesses about friction, and neither is a measurement of your joint. The tool also reports the implied nut factor — the K your μ_t and μ_b actually correspond to — which is the cleanest way to check whether the handbook K you were about to use is consistent with the friction you believe you have.
Then look at the scatter band. Torque control on an as-received joint typically achieves the target preload to about ±25–35%. That is not sloppiness in the tool; it is the spread of the friction coefficient across a batch of fasteners, multiplying straight through into clamp force. If the low end of the band is below the preload the joint needs to stay closed, or the high end is above proof load, torque control is not good enough for that joint and no amount of wrench calibration will fix it. The alternatives, in increasing order of cost and accuracy: angle control past snug (±10–15%), yield/gradient control, bolt elongation or ultrasonic measurement (±5%), hydraulic tensioning.
Finally, the utilisation figure. A bolt at 75% of proof load in pure tension is at 75% utilisation — but add the torsion the spanner is putting in and the von Mises equivalent can reach 90–95%. The torsion relaxes when the tool comes off, so the installed state is fine; the peak on the way there is what breaks the occasional fastener on a joint that “was only at 75%”.
Typical values
- Nut factor K: ≈0.20 dry/as-received steel, ≈0.15 lightly oiled, ≈0.10 waxed or with anti-seize, ≈0.18–0.25 for hot-dip galvanised (and much more variable). Zinc-flake and PTFE coatings are often specified with a friction window rather than a single value.
- Friction coefficients: 0.10–0.20 dry steel on steel, 0.08–0.14 lubricated, 0.04–0.10 waxed or coated. Thread and bearing values are frequently different — a hardened washer, a painted flange and an as-cast face are three different surfaces.
- Preload target: 60–75% of proof load is the usual design range for static joints; 75–90% is used where fatigue matters and the tightening method is accurate enough to support it.
- Scatter: ±25–35% torque control, ±10–15% angle control, ±5% stretch or ultrasonic measurement.
Worked example
An M12 × 1.75 property class 8.8 bolt, proof stress 640 MPa, tensile stress area 84.3 mm² from the thread standard, targeted at 75% of proof load. Assume K = 0.20 dry, or μ_t = μ_b = 0.14 with d₂ = 10.863 mm, d_n = 15.5 mm, β = 30°.
F_proof = 640 × 84.3 = 53 952 N = 53.952 kN
F = 0.75 × 53 952 = 40 464 N = 40.464 kN
σ = 40 464 / 84.3 = 480 MPa
Short form:
T = 0.20 × 40 464 × 0.012 m = 97.11 N·m
Long form, arm terms in mm:
pitch 1.75 / (2π) = 0.2785 mm
thread friction 0.14 × 10.863 / (2cos30°) = 0.8780 mm
head friction 0.14 × 15.5 / 2 = 1.0850 mm
total = 2.2416 mm
T = 40 464 × 0.0022416 m = 90.70 N·m
So 97.1 N·m or 90.7 N·m — a 7% disagreement between two defensible assumptions, and the implied nut factor from the friction values is 0.187, not the 0.20 assumed.
The thread-only arm is 0.2785 + 0.8780 = 1.1566 mm, so M_thread = 46 799 N·mm. With d_s = 10.360 mm and W_p = 218.3 mm³, τ = 214.3 MPa, and:
σ_v = √(480² + 3 × 214.3²) = √368 225 = 606.8 MPa → 94.8% of proof
At ±30% scatter the achieved preload lands somewhere between 28.3 kN and 52.6 kN, against a proof load of 53.95 kN. The joint has to work at 28 kN and survive at 53 kN. If it cannot do both, change the method, not the torque.
FAQ
Which method should I use — short form or analytical?
Use the short form when your fastener supplier has given you a measured K for that exact fastener and coating; it is the honest way to use test data. Use the analytical form when you want to see where the torque is going, when the joint face is unusual (large flange, soft washer, spherical seat), or when you are choosing a lubricant. Neither is more “correct” — they are the same physics with different amounts of the friction lumped together.
Why is my calculated torque different from the supplier’s chart?
Because the chart assumed a K, a preload fraction, and often a joint face, and probably did not tell you which. Back out the implied K from their torque and your stress area (K = T/(F·d)) and the difference is usually one of those three assumptions.
Does the tool cover reused, galled or hot-dip galvanised fasteners? No, and neither does any torque table. Reused fasteners have unknown thread friction, galling is a failure mode rather than a friction value, and hot-dip galvanised threads are notoriously variable unless waxed.
Why does utilisation exceed the preload percentage? Because tightening puts torsion into the shank as well as tension, and von Mises combines them. It is the reason “tighten to 90% of proof by torque” is a much more aggressive instruction than it sounds.
Can I use this for a structural bolt assembly? Only for understanding. Structural slip-critical assemblies are installed by turn-of-nut, direct tension indicators or calibrated-wrench procedures defined in the applicable specification, and those procedures — not a torque calculation — are what constitutes compliance.
Indicative figures for preliminary design and checking. Torque control sets preload indirectly and inaccurately; verify the tightening method, values and acceptance criteria against the fastener, joint and standards applicable to your work.