A bolt is a spring, and torque is only how you stretch it
A tightened bolt works by being stretched. The tension in it, called preload, clamps the joint members together, and it is that clamp force — not the bolt's shear strength — that stops the joint slipping, stops it leaking and stops the bolt fatiguing. A correctly preloaded bolt in a well-designed joint barely feels the external load at all, because the joint members unload faster than the bolt loads. That is the whole reason preload matters.
Torque is a proxy. You cannot see tension, so you measure the twisting effort needed to produce it. The trouble is that most of that effort goes into friction rather than into the bolt: roughly 50% is consumed under the nut face, roughly 40% in the threads, and only around 10% actually becomes bolt tension. Anything that changes friction changes the preload you get from a given torque, which is why the same torque figure produces very different results on dry, oiled and plated threads.
Hence the sequence used here. Decide the preload you want as a percentage of what the bolt can take, work out the force from the thread's tensile stress area and the grade's proof strength, and only then convert force into torque through the nut factor. Doing it in the other order — starting from a torque figure and hoping — is how joints end up either loose or yielded.
The three pieces of the calculation
Tensile stress area. A bolt does not break at the major diameter, nor at the minor diameter, but at an effective area between the two. Both ASME and ISO define it as At = 0.7854 (d − 0.9743/n)² for inch threads and 0.7854 (d − 0.9382 p)² for metric, where the bracketed term is the mean of the pitch and minor diameters. For a 1/2-13 that gives 0.1419 in², which is the number printed in every fastener table.
Proof load. Proof strength is the stress a bolt can carry with no measurable permanent set — conventionally around 85–90% of yield. SAE J429 assigns 55 ksi to Grade 2, 85 ksi to Grade 5 and 120 ksi to Grade 8; ISO 898-1 assigns 580 MPa to class 8.8 up to 16 mm diameter (600 MPa above it), 830 MPa to 10.9 and 970 MPa to 12.9. Multiply proof strength by the stress area and you have the proof load, the ceiling for elastic tightening.
The torque equation. T = K F d says the torque needed scales with the preload, with the bolt diameter, and with a nut factor K that absorbs everything frictional. K is not a coefficient of friction; it is an experimentally determined number for a whole assembly, and typical values run from about 0.10 for waxed threads to 0.30 for as-received galvanised. The convention values are 0.20 for plain dry steel and 0.15 for lubricated.
Because K appears as a simple multiplier, the torque is directly proportional to it. Lubricate a joint whose torque figure was derived for dry threads and the preload rises by the ratio of the two nut factors — going from K = 0.20 to K = 0.15 at unchanged torque raises preload by a third, which is exactly the mechanism by which carefully torqued stainless fasteners snap.
Worked example: 1/2-13 Grade 5, dry, to 75% of proof
A 1/2-13 UNC Grade 5 cap screw, plain steel threads, no lubricant, tightened to the usual 75% of proof load.
- Pitch. 1 ÷ 13 = 0.076923 in.
- Tensile stress area. 0.7854 × (0.5000 − 0.9743 × 0.076923)² = 0.7854 × (0.5000 − 0.074946)² = 0.7854 × 0.425054² = 0.7854 × 0.180671 = 0.14190 in².
- Proof load. 0.14190 × 85,000 = 12,062 lbf, which is the 12,050 lbf published for this size and grade.
- Target preload. 0.75 × 12,062 = 9,046 lbf, a bolt stress of 9,046 ÷ 0.14190 = 63.75 ksi.
- Torque. 0.20 × 9,046 × 0.500 = 904.6 lb·in = 75.4 lb·ft, which is 102.2 N·m.
Now oil the threads. With K = 0.15, the same 75.4 lb·ft produces a preload of 904.6 ÷ (0.15 × 0.500) = 12,061 lbf — exactly the proof load, with nothing in reserve. To hold 9,046 lbf on oiled threads you must reduce the torque to 0.15 × 9,046 × 0.500 ÷ 12 = 56.5 lb·ft. That 25% reduction is the single most useful thing this calculation tells you.
Choosing a preload target and reading the uncertainty
Seventy-five percent of proof load is the conventional target for reusable structural joints, and it is what most published torque charts assume. Permanent joints and gasketed flanges sometimes go to 85–90%, and joints that must resist fatigue benefit from high preload because a highly preloaded bolt sees only a fraction of the fluctuating external load. Below about 50% of proof, a joint under vibration is at real risk of self-loosening, which is the failure mode locking devices exist to address.
Read the torque range as the honest answer. Published studies of bolted joints put preload scatter under torque control at roughly ±25 to ±30%, dominated by variation in K rather than by wrench accuracy, and the band shown reflects that. A joint that would be damaged by 30% too much preload, or would fail at 30% too little, should not be assembled by torque alone. The alternatives are turn-of-the-nut, which measures rotation past snug and therefore measures stretch; direct bolt elongation with a micrometer or ultrasonics; load-indicating washers; and hydraulic tensioners.
Two grade cautions are worth naming. SAE Grade 2 is 55 ksi proof only from 1/4 in to 3/4 in; above that it drops to 33 ksi, so a large Grade 2 bolt is far weaker than the chart implies. And austenitic stainless has no proof load at all — ISO 3506 specifies tensile and yield strengths, not a proof load — so any stainless torque figure is derived from yield and should be treated as more approximate than a Grade 5 figure.
Tightening torque for UNC bolts at 75% of proof load, K = 0.20
| Size | At (in²) | Grade 2 (lb·ft) | Grade 5 (lb·ft) | Grade 8 (lb·ft) | Grade 5 preload (lbf) |
|---|---|---|---|---|---|
| 1/4-20 | 0.0318 | 5.5 | 8.5 | 11.9 | 2029 |
| 5/16-18 | 0.0524 | 11.3 | 17.4 | 24.6 | 3342 |
| 3/8-16 | 0.0775 | 20.0 | 30.9 | 43.6 | 4940 |
| 7/16-14 | 0.1063 | 32.0 | 49.4 | 69.8 | 6777 |
| 1/2-13 | 0.1419 | 48.8 | 75.4 | 106.4 | 9046 |
| 9/16-12 | 0.1819 | 70.4 | 108.7 | 153.5 | 11599 |
| 5/8-11 | 0.2260 | 97.1 | 150.1 | 211.9 | 14408 |
| 3/4-10 | 0.3345 | 172.5 | 266.5 | 376.3 | 21322 |
Grade 2 proof strength is 55 ksi only up to 3/4 in; above that SAE J429 drops it to 33 ksi, so do not extrapolate this column.
Tightening torque for coarse metric bolts at 75% of proof load, K = 0.20
| Size | At (mm²) | 8.8 (N·m) | 10.9 (N·m) | 12.9 (N·m) |
|---|---|---|---|---|
| M5 × 0.8 | 14.2 | 6.2 | 8.8 | 10.3 |
| M6 × 1.0 | 20.1 | 10.5 | 15.0 | 17.6 |
| M8 × 1.25 | 36.6 | 25.5 | 36.5 | 42.6 |
| M10 × 1.5 | 58.0 | 50.5 | 72.2 | 84.4 |
| M12 × 1.75 | 84.3 | 88.0 | 125.9 | 147.1 |
| M16 × 2.0 | 157 | 218.1 | 312.1 | 364.7 |
Above 16 mm, ISO 898-1 raises the class 8.8 proof stress to 600 MPa, so figures extrapolated beyond this table will be low by about 3%.
Where torque control goes wrong
- Applying a dry-thread torque to lubricated threads. Preload is inversely proportional to K, so oiling a joint torqued to a dry figure raises tension by the ratio of the nut factors — enough to yield a bolt tightened to 75% of proof.
- Torquing through a locking nut or a plated surface without accounting for it. Prevailing-torque nuts consume torque that never becomes preload, so the running torque must be measured and added to the calculated figure.
- Ignoring the under-head condition. About half of the applied torque is consumed under the nut or bolt head, so a washer, a rough spot face, or a burr changes the answer as much as thread lubrication does.
- Reusing a bolt that has been tightened past yield. Once a bolt has yielded, its stress area is reduced and its remaining proof load is unknown. Yield-tightened bolts are single-use by definition.
- Assuming the wrench is the uncertainty. A calibrated click wrench is typically within a few percent; the nut factor is not. Improving wrench accuracy without controlling friction improves almost nothing.
- Torquing to a chart when the joint is soft. Gaskets, plastics and long grip lengths relax after assembly, so the preload measured hours later is lower than the preload achieved. Re-torque or design for relaxation.
Where the torque method sits among the alternatives
Torque control is the least accurate of the common preload methods and by far the most convenient, which is why it dominates. Turn-of-the-nut is the next step up: after snugging, a defined additional rotation stretches the bolt by a calculable amount, so the method measures displacement rather than friction and is much less sensitive to lubrication. Bolt elongation measurement, whether with a micrometer over a machined bolt or with ultrasonics, measures the thing you actually want. Hydraulic tensioners pull the bolt directly and let you run the nut down against a known load.
Whatever method you use, the joint design must come first. A grip length of at least four or five diameters makes the bolt a softer spring and dramatically improves fatigue behaviour; a stiff, short bolt in a soft joint is the worst combination. Engagement length in a tapped hole should be at least one diameter in steel and more in aluminium, so that the bolt, not the female thread, is the member that fails — and the female thread's own strength depends on the tap drill that produced it, which the tap drill size calculator resolves.
Where the fastener passes through a machined hole rather than a threaded one, the clearance and the fit class matter to how the joint carries shear; the ISO hole and shaft fit calculator handles that side. And if you are producing the parts yourself, the holes come first — the drilling speed and feed calculator covers the speeds, feeds and torque that drilling them will demand. The strength values used here come from SAE J429 for inch fasteners and ISO 898-1 for metric property classes.