SizingKitMechanical · Threaded fasteners
Bolt torque, and the friction that decides it
Pick a thread and a grade and this returns the tightening torque in pound-feet and newton-meters for a stated fraction of proof load, built from the tensile stress area in ASME B1.1 or ISO 898-1 and the proof stress in SAE J429 or ISO 898-1. It then does the thing a torque chart cannot: it takes that one torque figure and shows what it produces on the same bolt in each of seven published surface conditions, from half the intended preload to half again above proof load. Free, no signup, and the nut factor K is on the screen as an editable number rather than hidden inside the answer.
- 100% free
- No signup
- SAE J429 and ISO 898-1
- K shown, not hidden
- Stretch and angle too
The fastener and the joint
Two of the three terms in T = K·D·F are known exactly. The picker below chooses them; the third is a friction coefficient, and the rest of this page is about how little it is known.
Grades follow the system: inch threads take the SAE J429 grades, metric threads the ISO 898-1 property classes. The two are not interchangeable.
Stress area 0.1419 in² / 91.55 mm², from the thread table rather than from the shank.
Three radial lines on the head. Proof 85,000 psi / 586 MPa, SAE J429.
Default 75% — The long-standing design practice for fasteners intended to be reused, printed in Machinery's Handbook and in the major fastener manufacturers' engineering guides: preload to 75% of proof load. A joint that will never be taken apart is often taken to 90%, which leaves almost nothing for the friction spread the table below prices.
The default in every published torque chart, and the least repeatable case — 'as received' covers everything from oily to rusty.
Prefilled with 0.2 for the condition above, whose published band is 0.2 to 0.3. If your fastener supplier publishes a K for the coating on the part in your hand, that figure beats this one.
The clamped thickness the bolt stretches over. It changes nothing about the torque and everything about how measurable the stretch is.
TIGHTENING TORQUE
75.4 lbf·ft
102.2 N·m
TARGET PRELOAD
9,046 lbf
40.2 kN · 75% of 12,061 lbf proof
BOLT STRETCH
4.4 thou
111.7 µm · 21° of nut on a rigid joint
For this condition the published band is K 0.2 to 0.3, so the torque that reaches 9,046 lbf is anywhere from 75.4 lbf·ft to 113.1 lbf·ft — 153 N·m against 102 N·m. That spread is the band alone, before the ±25% scatter that sits inside any single value of K.
THE SAME 75.4 LBF·FT ON THE SAME BOLT
| Condition | K | Preload | Of proof |
|---|---|---|---|
| Plain steel, as received, dry | 0.2 | 9,046 lbf | 75% |
| Zinc plated, dry | 0.2 | 9,046 lbf | 75% |
| Hot-dip galvanized, dry | 0.3 | 6,031 lbf | 50% |
| Lubricated (oil or grease) | 0.15 | 12,061 lbf | 100% |
| Cadmium plated | 0.13 | 13,917 lbf | 115% |
| Molybdenum disulfide or anti-seize | 0.12 | 15,077 lbf | 125% |
| PTFE coated or waxed | 0.1 | 18,092 lbf | 150% |
Read the table above as the answer rather than the caveat. Apply 75.4 lbf·ft to this fastener in 3 of these conditions — cadmium plated; molybdenum disulfide or anti-seize; ptfe coated or waxed — and the tension goes past proof load, up to 150% of it. The bolt takes a permanent set on assembly and nothing on the outside of the joint shows it. This is what happens when somebody reads a dry torque chart and then oils the threads to get the nut to run down easily, and it is the commonest way a fastener is destroyed before the machine has ever run.
K is a lumped empirical factor, not a coefficient of friction and not a property of the bolt. It changes with plating, lubricant, surface roughness, washer, the number of previous tightenings, the speed of tightening and the temperature, and it carries about ±25% scatter even when every one of those is held constant. That scatter passes straight into preload: torque control is the least accurate of the common preload methods. If preload matters, measure it — angle control, bolt elongation, load-indicating washers or ultrasonic measurement — rather than trusting a torque figure derived here. The relation itself is the short-form torque-tension equation: Published nut-factor bands for the standard surface conditions, as they appear in fastener manufacturers' engineering guides and in the torque-tension literature. The relation itself, T = K·D·F with D the nominal diameter, is the short-form torque-tension equation used throughout that literature.
Where the preload genuinely matters, measure it instead of inferring it. The stretch figure above — 4.4 thou over 2 in of grip — is what a bolt micrometer or an ultrasonic gauge reads directly, and it does not care what the threads were coated with. The angle beside it, 21°, is that stretch expressed as nut rotation over a pitch of 76.9 thou on a perfectly rigid joint; a real joint compresses too, so the turn-of-nut angle is always larger. The tabulated angles for structural work are in the RCSC Specification for Structural Joints, which this site does not reproduce — take them from the specification rather than from the number here.
Stretch is worked at the tensile stress area over the whole grip, at 29,000,000 psi. E = 29,000 ksi, the value AISC specifies for structural steel design. Effectively identical for every carbon and alloy steel, hardened or not — heat treatment changes strength, not stiffness. This surprises people: a Grade 8 bolt stretches exactly as much as a Grade 2 bolt under the same load. That last point catches people out on this page in particular: changing the grade above changes the torque, because it changes the proof load, and changes the stretch not at all for a given tension. A bolt with a plain shank inside the grip is stiffer than this figure suggests and stretches less.
The stress area comes from the thread table rather than being recomputed here — pitch, diameters and the designation are one page and this is another, and both read the same ASME B1.1 and ISO 898-1 geometry. A tightened bolt is a stiff spring in series with the joint it clamps, which is the whole reason preload works: the external load is shared between the two in proportion to their stiffnesses, and a preloaded bolt sees only a fraction of the cycle that would otherwise pass through it. That is also why the tie rods on a hydraulic cylinder are torqued to a specification rather than to feel. None of this is a stamped design: joint stiffness, gasket creep, fatigue and any structural connection are for the fastener manufacturer’s data and a qualified engineer.
How to turn a grade and a diameter into a torque figure worth using
Two terms of T = K·D·F are exact and the third is not. The method is to make the third one visible.
Pick the thread, and let the grade list follow it
Choose the Unified inch or ISO metric system and then the designation. The tensile stress area comes with it out of the thread table, which is the right area for a bolt in tension — not the shank and not the minor diameter. Only the grades that actually cover that diameter are then offered, because SAE Grade 2 and Grade 5 and ISO class 8.8 each get weaker above a size: a 1-1/4 in Grade 5 has a proof stress of 74,000 psi and not the 85,000 psi of its smaller brother, and using the wrong row overstates the load it can hold by 15%.
Set the target preload as a fraction of proof load
Proof load is the tension a fastener takes without measurable permanent set, so it is the ceiling. The prefilled 75% is the long-standing figure for fasteners meant to be reused; 90% is used for permanent connections and leaves almost nothing for the scatter that follows. Neither is a specification — structural steelwork pretensions to a stated minimum from the RCSC specification instead, and a critical joint is tightened by angle or by measured stretch rather than by torque at all.
Choose the surface condition, then read the table below the answer
The condition sets the nut factor K, which the field beside it prefills and which you can overwrite with whatever your fastener supplier publishes for the coating on the part in your hand. The torque appears above. Underneath it is the table that matters: the same torque applied to the same bolt in each of the seven published conditions, with the resulting preload as a percentage of proof. On a 1/2-13 Grade 5 that runs from 50% to 150%, and the top of it is a bolt that has yielded during assembly.
Technical specifications
| Relation | T = K·D·F, the short-form torque-tension equation, with D the nominal diameter and F the target preload. Not physics: a one-term empirical fit in which K stands in for friction under the head and in the threads at once |
|---|---|
| Tensile stress area | Read from the thread table, not recomputed — ASME B1.1 Appendix B, 0.7854(D − 0.9743/n)², for the Unified series and ISO 898-1, 0.7854(D − 0.9382P)², for metric. 1/2-13 UNC is 0.1419 in²; M12×1.75 is 84.27 mm² |
| Grades offered | SAE J429 grades 2, 5 and 8 for inch threads and ISO 898-1 classes 4.6, 5.8, 8.8, 10.9 and 12.9 for metric, as specified minimums. Two-row grades are filtered by diameter, so a 1-1/4 in bolt cannot be given the 85,000 psi proof stress that stops at 1 in |
| Nut factor K | Seven published conditions from 0.08 for a waxed or PTFE-coated fastener to 0.35 for hot-dip galvanized, each a band rather than a value. Prefilled from the condition and editable, because K belongs to a fastener in a hole on a day, not to a fastener |
| Scatter | About ±25% in the resulting preload with the condition held constant, on top of the width of the band itself. That is why torque control ranks below angle, stretch measurement, load-indicating washers and ultrasonic methods for any joint that matters |
| Stretch and angle | Elongation is F·L/(A·E) over the entered grip at 29,000,000 psi, which suits a fully threaded fastener and overstates a bolt with a plain shank in the grip. The angle beside it assumes a perfectly rigid joint, so a real turn-of-nut figure is always larger |
| Worked example | 1/2-13 UNC, SAE Grade 5, plain and dry at K = 0.20, 75% of proof: stress area 0.1419 in², proof load 12,061 lbf, target preload 9,046 lbf, torque 75.4 lbf·ft or 102 N·m, stretch 4.40 thou over a 2 in grip, and 21° of nut rotation on a rigid joint |
| The same torque elsewhere in the table | That 75.4 lbf·ft gives 6,031 lbf on a hot-dip galvanized bolt (50% of proof), 12,061 lbf lubricated (100%), 15,077 lbf with anti-seize (125%) and 18,092 lbf waxed (150%). Three of the seven conditions put the fastener past proof at the figure a dry chart printed |
Frequently asked questions
Should I use the dry torque figure on a bolt I have oiled?
No, and doing it is the single commonest way a fastener is destroyed before the machine runs. A dry plain-steel chart is written around K near 0.20; oil or grease takes K to about 0.15 and an anti-seize or a waxed fastener to 0.10. Since preload is torque divided by K times diameter, halving K doubles the tension. Applying the 75 lbf·ft that suits a dry 1/2-13 Grade 5 to the same bolt with anti-seize on it produces 15,077 lbf of preload against a proof load of 12,061 — 125% of proof, so it has taken a permanent set, and nothing on the outside of the joint shows that it happened.
How accurate is torque as a way of getting preload?
It is the least accurate of the methods in common use, and the arithmetic explains why rather than excusing it. Of the torque you apply, only about 10% ends up as tension: roughly 40% is lost to friction under the turning head or nut and roughly 50% to friction in the threads. K is a single lumped stand-in for both of those, so the answer is dominated by the term nobody measured. Even with the condition fixed, published guidance puts about ±25% scatter on the resulting preload. Angle control, measured bolt elongation, load-indicating washers and ultrasonic measurement all beat it, in that rough order of cost.
Why does a torque chart give a different number from this page?
Almost always because it assumed a K you did not, and often because it assumed a different fraction of proof. Published charts are usually built at K = 0.20 dry and either 75% or 65% of proof, and a manufacturer's own chart may use its own tested K for its own coating. This page makes both assumptions visible and editable rather than baking them in, so if you have a figure that disagrees, change the two boxes to match its assumptions and see whether the disagreement survives. If it does, the difference is in the stress area or the grade row, and both are printed here with the standard they came from.
Does a fine thread take more torque than a coarse one?
Slightly more, because it is a slightly stronger bolt, not because the thread is finer. A fine thread removes less metal, so its tensile stress area is larger — 0.1599 in² for 1/2-20 UNF against 0.1419 in² for 1/2-13 UNC, about 13% more — and at the same grade and the same fraction of proof it therefore carries 13% more preload and wants 13% more torque. The nut factor in the short-form relation does not distinguish between the two at all, which is one of the honest limitations of the method: a more detailed model separates thread friction from under-head friction and does see the helix angle.
Can I use these numbers on stainless or on a plated structural bolt?
Not the grades, and be careful with K. SAE J429 and ISO 898-1 cover carbon and alloy steel only; a stainless fastener runs to ISO 3506 and is far weaker — an A2-70 is roughly equivalent to a class 6.8 — so a grade row from this table will overstate what it holds. Stainless also galls, which is why anti-seize is normally specified on it, and that moves K to the bottom of the range at the same time. Hot-dip galvanized structural bolts are the mirror image: the coating is thick and rough, K rises to 0.25–0.35 and gets much more variable, which is why they are usually supplied lubricated and tested as a lot.
What is the angle figure for, and why is it smaller than a turn-of-nut spec?
It is the nut rotation that would produce the calculated stretch if the clamped parts were infinitely rigid, and it is smaller than a real turn-of-nut specification because they are not. A real joint compresses under the same preload, so part of the rotation goes into squashing the members rather than stretching the bolt, and the required angle is larger — how much larger depends on the joint's stiffness relative to the bolt's. Tabulated angles for structural work live in the RCSC Specification for Structural Joints; this site does not reproduce them, so take yours from the specification and treat the figure here as showing the order of magnitude.
Why does the torque change when I switch the grade but the stretch does not?
Because grade sets strength and every steel has the same stiffness. Proof stress rises from 55,000 psi at SAE Grade 2 to 120,000 psi at Grade 8, so the target preload and therefore the torque more than double; Young's modulus stays at 29,000,000 psi throughout, because heat treatment changes what a steel can survive and not how far it stretches under a given load. The practical consequence is that a Grade 8 bolt at 75% of its proof load stretches more than a Grade 2 at 75% of its own — the tension is higher — but at the same tension the two are indistinguishable on a stretch gauge.
About preload, and why torque is a poor way to get it
The point of tightening a bolt is not to make it tight, it is to put a specific tension into it. A preloaded joint carries an external load mostly as a reduction in the clamping force between its members rather than as an increase in the tension in the fastener, so a bolt that has been properly preloaded barely feels the fatigue cycle that would otherwise pass straight through it, and the joint does not work loose. Everything else follows from that: the target is a fraction of proof load, proof load is the tensile stress area times the proof stress the grade specifies, and the stress area is a defined geometric quantity that the thread tables already carry. Two of the three terms in the calculation are therefore exact, and if there were a reliable way to reach a stated tension there would be nothing interesting left to say.
The trouble is the third term. Torque is not tension; it is what you have to supply to overcome three things at once — the friction under the turning head or nut, the friction on the thread flanks, and the helix that actually does the useful work. Of the torque applied to an ordinary fastener, roughly 40% is spent under the head, roughly 50% in the threads and only about 10% goes into stretching the bolt. The short-form relation T = K·D·F lumps all of that into a single coefficient, and K is not a coefficient of friction and not a property of the bolt: it moves with plating, with lubricant, with surface finish, with whether there is a washer, with how many times the fastener has been tightened before, and with temperature. Across ordinary conditions it runs from 0.08 to 0.35, so two identical bolts taken to identical torque, one dry and one waxed, differ by more than three times in preload. Even with the condition pinned down, about ±25% of scatter remains. That is the honest accuracy of a torque wrench specification, and it is why this page prints a band and a comparison table rather than a single number in bold.
What most calculators get wrong is not the arithmetic, which is trivial, but the framing: they present K = 0.2 as a default rather than as an assumption about a surface, and they do not say what happens when the assumption is wrong. It is wrong constantly — anti-seize on stainless to stop it galling, a zinc flake coating specified after the drawing was issued, a fastener that has been out once already. The remedies are all measurements rather than better constants. Bolt elongation, printed on this page beside the torque, is read directly with a bolt micrometer or an ultrasonic gauge and does not care what the threads were coated with. Turn-of-nut converts a known angle past snug into a known stretch, and the structural values live in the RCSC specification rather than here. A load-indicating washer shows preload as a squashed bump. Where none of those is available, tightening a stiff spring in series with a stiffer joint by torque alone remains the trade’s working compromise — and knowing its real spread is what separates a specification from a guess. Nothing on this page is a stamped design: joint stiffness, gasket creep, fatigue life and any structural connection belong to a qualified engineer and to the fastener manufacturer’s published data.
Where the torque spec you build goes
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Threads, grades, coatings and the K values you overwrite are held in this tab and nowhere else — no login, no saved specification list, and nothing recorded about which fastener a given customer’s assembly runs on.