Bolt Torque Calculator

T = K·F·d, with the nut factor computed from friction rather than looked up, the torque split into the three terms it is made of — about half into friction under the head, two fifths into the thread, a tenth into stretching the bolt — and the preload band the chosen tightening method actually delivers printed beside the single torque figure. Every published nut factor this batch could source is tabulated and attributed.

Last updated 24 Sep 2026

Bolt torque

Size, class, target and method → torque and its band

Thread sizeMetric coarse to ISO 261, then Unified coarse. The stress area of a metric thread uses ISO 898-1’s 0.938194 constant and an inch thread uses the Unified 0.974279 — they are genuinely different numbers, for the reason the stress-area page explains.

Property class or gradeISO 898-1 for metric, SAE J429 for inch, ISO 3506-1 for stainless. Stainless has no stress under proof load at all, so a stainless bolt is preloaded against its 0.2% proof strength and the page says so.

Target preload, % of the proof stress75% for a fastener that will be undone again and 90% for a permanent one, which is Machinery’s Handbook’s rule as quoted by Sandia. A torque-controlled joint is often specified at 65–75% precisely because of the scatter below.

Where the nut factor K comes fromComputing it from friction is the honest option, because K is not a property of the bolt. The published values are all here too, attributed, and they disagree with each other.

Thread friction coefficient μ0.10–0.16 for a lubricated or plated steel thread, 0.12–0.20 dry, higher for stainless on stainless, which galls. VDI 2230 tabulates classes A to E.

Underhead or nut-face friction coefficient μThe one that matters most: about half the torque goes here. A hardened washer under the turned element lowers it and makes it repeatable, which is most of what a washer is for on a high-duty joint.

K, if you are entering itA K measured on your own joint beats every published figure. Portland Bolt put it plainly: torque values that claim to relate torque to pretension without verification shall not be used.

Tightening method, for the preload bandVDI 2230 Table A8. The band is what this method’s tightening factor α implies, and it is the number this page exists to print beside the torque.

Not a circuit: two bar scales. The top three bars are the three terms the tightening torque is made of, all to one scale in per cent — friction under the head or nut face, friction in the thread, and the sliver that actually stretches the bolt. They are computed from the thread geometry and the bearing-face geometry at the friction coefficients you entered, not read off a table, and at 0.15 on both surfaces they come out at about 48 / 39 / 12 against the 50 / 40 / 10 that Nord-Lock publish. Watch the third bar when you change the friction: it is the only one doing useful work and it is always the shortest. The lower scale is the answer this page exists to give. The shaded band is the preload that ONE torque figure actually delivers, as a percentage of the bolt's proof load, for the tightening method you chose; the single line inside it is the target you asked for and the line at 100 is the proof load. A band that reaches past 100 means part of the population will take a permanent set.

49.98N·mExample

M10 class 8.8, 75% of proof load, friction 0.15 on the thread and 0.15 under the nut, tightened with a torque wrench on an estimated friction coefficient

One line, and then the honest part

T = K · F · d · K = [ P/2π + 0.5 d₂ μ_G / cos 30° + 0.5 D_Km μ_K ] / d · F_target = (pct/100) · A_s · S_p · F ranges from 2F/(1+α) to 2αF/(1+α)

T: tightening torque at the nut or the head. What a wrench measures, and the only thing in this calculation you can read off an instrument
F: preload — the tension in the bolt and the clamp load on the joint. What you actually want, and what nothing on the wrench measures
K: the nut factor. Not a constant, not a material property, and about nine tenths friction. It is the whole problem
d: nominal thread diameter. Note that K is defined against d and not against the pitch diameter or the bearing diameter, which is why K drifts slightly with size even at fixed friction
P: thread pitch. The P/2π term is the only one that does useful work — it is the torque a frictionless screw would need
d₂: pitch diameter, where the thread friction acts. The 0.5/cos 30° = 0.577 is VDI 2230’s 0.58, written out
D_Km: mean diameter of the bearing face, (d_w + d_hole)/2. Half the torque is spent here, which is why a hardened washer under the turned element is not decoration
S_p: stress under proof load, from ISO 898-1 or SAE J429. Stainless has none, so a stainless bolt is preloaded against its 0.2% proof strength
α: VDI 2230’s tightening factor, F_max/F_min for the method. The band above is the arithmetic mean split by it

Worked example

M10 class 8.8, 75% of proof load, friction 0.15 on the thread and 0.15 under the nut, tightened with a torque wrench on an estimated friction coefficient
Stress area A_s = (π/4)(10 − 0.938194 × 1.5)² = 57.99 mm². Proof stress for class 8.8 up to M16 is 580 N/mm², so the proof load is 33.63 kN
Target preload at 75% = 25.23 kN. That is Machinery's Handbook's figure for a fastener that will be undone again; 90% is the permanent-joint figure
The three torque terms, in millimetres of effective radius: pitch P/2π = 0.2387, thread friction 0.5 × 9.026 × 0.15/cos 30° = 0.7817, underhead friction 0.5 × 12.815 × 0.15 = 0.9611. They sum to 1.9815 mm
So K = 1.9815 / 10 = 0.1982 — which is the 0.20 that both Portland Bolt and Fastenal publish for a plain or zinc-plated bolt, arrived at from friction rather than from a table
And the split: 48.5% of the torque goes into friction under the nut face, 39.4% into friction in the thread, and 12.0% into stretching the bolt. Nord-Lock publish 50 / 40 / 10; this is the same answer, computed
T = K F d = 0.1982 × 25,225 N × 0.010 m = 49.98 N·m, or 36.9 lbf·ft
NOW THE PART THAT MATTERS. A torque wrench set on an estimated friction coefficient has a VDI 2230 tightening factor of 1.6 to 2.0, which is ±23% to ±33%. At α = 2.0 this 49.98 N·m delivers somewhere between 16.82 kN and 33.63 kN — the top of that band IS the proof load. The answer to “what torque?” is not 50 N·m; it is 50 N·m for a preload between 17 and 34 kN, and if the joint needs 25 kN guaranteed you need a bigger bolt or a better method

Every published nut factor this batch could source, and who publishes it

Two things to read here. The first is the spread: the same target clamp load on the same M10 needs 25 N·m waxed and 63 N·m hot-dip galvanised, a factor of 2.5, and nothing about the bolt has changed. The second is that the two publishers do not agree with each other. Fastenal put “zinc and dry conditions” at 0.20; Portland Bolt put plain unplated steel at 0.20 and hot-dip galvanising at 0.25. Neither of them puts a zinc coating BELOW plain steel — galvanising raises friction, it does not lower it. Nothing here is averaged. Portland Bolt also give the outer bound: K “can range from 0.10 for a well lubricated/waxed assembly, to over 0.30 for one that is dirty or rusty”. The same designation can mean different dimensions in different standards families — ANSI against ISO, inch against metric, one national standard against another. The family used here is named beside every figure; check which one your part was made to.
Condition	Published by	K	Torque for 25.2 kN on an M10 (N·m)	% of the plain-steel figure
Waxed — pressure wax as supplied on high-strength nuts	Portland Bolt	0.10	25.2	50
PTFE / proprietary coating on nut, bolt and washer	Fastenal	0.12	30.3	60
Lubricated — oil or tapping fluid	Fastenal	0.15	37.8	75
Anti-seize, thread locker, or some plain conditions	Fastenal	0.17	42.9	85
Plain, unplated, as received, slightly oily	Portland Bolt	0.20	50.5	100
Zinc plated, and dry conditions	Fastenal	0.20	50.5	100
Hot-dip galvanised	Portland Bolt	0.25	63.1	125

Where the torque goes, computed size by size at μ = 0.15

This is the table that replaces the sentence everybody quotes. Nord-Lock state the split as 50% underhead, 40% thread, 10% useful, and this page does not take that on trust — it evaluates VDI 2230’s three torque terms from the thread geometry and the bearing-face geometry at every size and gets 47–49% underhead, 38–42% thread and 9–14% useful, averaging 48 / 41 / 11. The published split is right, and now it is derived rather than asserted. Two consequences follow directly. Lubricating the bearing face matters about as much as lubricating the thread, because they are similar terms. And the reason K is not a material constant is that nine tenths of it is friction, which is a property of the surfaces on the day. This is a first-pass calculation on an idealised part — uniform section, static load, no stress raisers beyond those stated, and room-temperature material properties. Real parts have fillets, keyways, surface finish and duty cycles that a closed-form answer cannot see.
Size	K	Underhead friction (%)	Thread friction (%)	Stretching the bolt (%)	Torque for 75% of proof, class 8.8 (N·m)
M4	0.2019	48.2	38.0	13.8	3.1
M5	0.1959	47.4	39.6	13.0	6.0
M6	0.2005	48.3	38.5	13.2	10.5
M8	0.1994	48.5	39.0	12.5	25.4
M10	0.1982	48.5	39.4	12.0	50.0
M12	0.1942	47.7	40.4	12.0	85.4
M14	0.1941	47.8	40.5	11.7	136.4
M16	0.1920	48.2	41.4	10.4	209.4
M18	0.1933	47.8	40.8	11.4	291.3
M20	0.1917	48.1	41.5	10.4	408.3
M22	0.1916	48.7	41.9	9.4	556.2
M24	0.1910	47.9	41.7	10.4	703.1
M27	0.1901	48.4	42.3	9.3	1,025.8
M30	0.1908	48.3	42.0	9.7	1,395.8
M36	0.1898	48.4	42.3	9.3	2,427.7

The same 25.2 kN target, by tightening method — VDI 2230 Table A8

The scatter column here is not a second set of published numbers. It is exactly (α − 1)/(α + 1), at every one of the thirteen rows in VDI’s own table, which is how this batch confirmed it had read the table’s columns in the right order before using any of it. Read the last column and the cost of a cheap method is plain: estimate the friction and set a torque, and you can only count on 50–63% of what you aimed for. The preload accuracy by tightening method calculator turns that into how much more clamp load a better method buys from the same bolt. These dimensions come from a published standard’s table, not from a formula. The standard itself is cited below and the printed values are attributed to the catalogue they were taken from; a different publisher may round differently in the last digit.
Method	Tightening factor α	Scatter it implies (%)	Lowest preload (kN)	Highest preload (kN)	Guaranteed fraction of target (%)
Ultrasonic length measurement	1.1 – 1.2	±5 – 9	22.9	27.5	83
Mechanical elongation, pressure screws	1.1 – 1.3	±5 – 13	21.9	28.5	77
Mechanical elongation measurement	1.1 – 1.5	±5 – 20	20.2	30.3	67
Hydraulic tensioning	1.1 – 1.4	±5 – 17	21.0	29.4	71
Multipartite nut with a threaded bushing	1.2 – 1.5	±9 – 20	20.2	30.3	67
Yield-point controlled	1.2 – 1.4	±9 – 17	21.0	29.4	71
Rotation-angle controlled (torque plus angle)	1.2 – 1.4	±9 – 17	21.0	29.4	71
Hydraulic impulse driver	1.2 – 2.0	±9 – 33	16.8	33.6	50
Torque-controlled hydraulic, gradual	1.4 – 1.6	±17 – 23	19.4	31.0	63
Torque wrench, dynamic measurement, torque found by test	1.4 – 1.6	±17 – 23	19.4	31.0	63
Torque-controlled, friction coefficient ESTIMATED	1.6 – 2.0	±23 – 33	16.8	33.6	50
Torque-controlled, friction estimated, rough surfaces	1.7 – 2.5	±26 – 43	14.4	36.0	40
Impact wrench or hand tightening	2.5 – 4.0	±43 – 60	10.1	40.4	25

What this page deliberately does not do

The one thing worth repeating: a manufacturer’s torque specification, or a design code’s, beats this page every time. A cylinder head, a wheel nut, a flange to ASME PCC-1, a structural connection to AISC or EN 1090 — all of those have a published torque or a published procedure that was validated on the real joint, which is something no general formula can be. This page sizes a part; it does not certify one. Where the answer carries a consequence — a load path, a lifting duty, a pressure boundary, a fastener holding something that can fall — confirm it against the design code that governs the application, and against the manufacturer’s own rating, before relying on it.
What	Why	Where instead
Print a torque table you can use without reading anything	That table is the thing this page exists to replace. A torque without a stated K, a stated preload target and a stated scatter is three unstated assumptions wearing one number	Everything the table would contain is above, with each assumption on its own line and adjustable.
Recommend a K for your joint	K is a property of your surfaces, your lubricant and your washer, measured on the day	The published values are tabulated and attributed above, and the friction route lets you put in what you measured. Portland Bolt’s own instruction is to determine it by experiment.
Compute the stress area or the proof load from first principles	One page should own that	The proof load and tensile stress area calculator, which derives ISO 898-1’s 0.938194 rather than quoting it.
Tell you how deep the tapped hole has to be	A torque is useless if the thread strips first	The thread engagement length calculator.
Hex key, socket and driver sizes; tap drill and clearance drill diameters; pitch to threads per inch	Those are tool and size questions, not features on a part	This site already has a hex key and socket size page, and the converters plugin owns the drill sizes and the pitch/TPI series. Neither is duplicated here.

Why the nut factor is the whole problem, and why the answer is a band

Almost every page that answers “what torque for an M10?” prints a number and hides three assumptions inside it. The assumptions are what preload is being aimed at, what friction is being assumed, and how wrong the answer is. This page prints all three, because the number on its own is not useful and is sometimes dangerous. T = K·F·d is the whole formula. K — the nut factor — is the whole problem.

K is not a property of the bolt. VDI 2230 writes the tightening torque as three terms: a pitch term P/2π that would exist on a frictionless screw, a thread friction term 0.58·d₂·μ_G, and a bearing-face friction term 0.5·D_Km·μ_K. Divide their sum by d and you have K. Evaluate it for an M10 at a friction coefficient of 0.15 in both places and it comes out at 0.198 — which is the 0.20 that Portland Bolt publish for a plain bolt and Fastenal publish for a zinc-plated one. The published number is right; it just is not a constant. Change the surfaces and it moves between 0.10 and over 0.30, and the same torque then delivers a preload that differs by a factor of three.

Where the torque goes is the paragraph people remember. Nord-Lock state it as 50% into friction under the head or nut face, 40% into friction in the thread, and 10% into actually stretching the bolt. This page does not take that on trust: it evaluates the three terms at every size in the table below and gets 47–49%, 38–42% and 9–14%, averaging 48 / 41 / 11. So the published split is correct, and now it is derived. Two things follow. Lubricating the bearing face is worth about as much as lubricating the thread, because the two terms are similar in size — which is most of what a hardened washer under the turned element is for. And since nine tenths of K is friction, K is a property of the day, the surfaces and the lubricant, not of the fastener.

The honest headline is a band, not a number. VDI 2230’s Table A8 gives a tightening factor α = F_max/F_min for each tightening method; for a torque wrench set on an estimated friction coefficient it is 1.6 to 2.0, which is ±23% to ±33% about the mean. The NASA Fastener Design Manual reproduces two other published tables that say much the same: the Industrial Fasteners Institute put a torque wrench at ±25%, Machine Design put torque control at ±15 to ±30%, and Sandia’s guideline puts an unlubricated bolt at ±35%. So 50 N·m on an M10 class 8.8 is not “25 kN of clamp load”. It is somewhere between 17 and 34 kN, and the top of that band is the bolt’s proof load. Design for the bottom, check the bolt at the top, and if the gap is unacceptable the fix is a better tightening method rather than a more confident table — the preload accuracy by tightening method calculator computes what each one buys you.

What this page needs from elsewhere, and what needs it. The stress area and the proof load come from the proof load and tensile stress area calculator, which derives ISO 898-1’s 0.938194 constant rather than quoting it. A torque is worthless if the tapped hole strips first, which is the thread engagement length calculator. Why a preloaded bolt barely feels an external load is the bolted joint stiffness and separation calculator, and why raising preload usually helps fatigue rather than hurting it is the bolt fatigue under alternating load calculator. If the load is in shear rather than tension, the bolt group shear calculator is the page, and the answer there is usually that the plate fails before the bolt does.

Frequently asked questions

What torque should I use on an M10 class 8.8 bolt?

About 50 N·m if you want 75% of proof load, if the nut factor really is 0.20, and if you accept that the preload you get will be somewhere between about 17 and 34 kN rather than the 25 kN you aimed at. Every one of those conditions is doing work. Waxed threads at K = 0.10 need 25 N·m for the same clamp load and hot-dip galvanised ones at K = 0.25 need 63. If the joint has a published torque from the machine’s maker or from a design code, use that instead — it was measured on the real joint, which is the only way the number can be known.

Why does lubrication change the torque so much?

Because about 90% of the torque is fighting friction and only about 10% is stretching the bolt. The table on this page computes the split from the thread and bearing-face geometry at every size: roughly 48% under the head or nut, 39% in the thread, 12% useful. Halve the friction and you roughly halve the torque needed for the same preload. Which also means the reverse: apply a dry-bolt torque to a lubricated one and you can put nearly twice the intended preload into it.

How accurate is torque as a way of setting preload?

Poor, and the published figures agree about that. VDI 2230’s tightening factor for torque control with an estimated friction coefficient is 1.6 to 2.0, which is ±23% to ±33%. The Industrial Fasteners Institute put a torque wrench at ±25%; Machine Design put torque control at ±15 to ±30%; Sandia’s guideline gives ±35% unlubricated, ±30% cadmium plated and ±25% lubricated. Measuring the bolt’s stretch instead gets you to ±5 to 20% and ultrasonic length measurement to ±5 to 9%. The practical consequence is that a torque-controlled joint can only be designed for the bottom of its band, which wastes most of the bolt.

Is the nut factor K the same as the coefficient of friction?

No, and conflating them is a common error. μ is a property of two surfaces. K is a lumped geometric-and-frictional coefficient defined by T = K F d, so it depends on the pitch, the pitch diameter, the bearing-face diameter and the hole diameter as well as on two different coefficients of friction. This page computes K from those, which is why it can also tell you where the torque went. As a rough guide the two are numerically close for a hex-head steel bolt — μ of 0.15 gives K near 0.20 — but that coincidence is not a relationship.

Should I torque to 75% or 90% of proof load?

Machinery’s Handbook, as quoted in Sandia’s bolted joint guideline, says 75% of the proof strength for removable fasteners and 90% for permanent ones. A torque-controlled joint is often specified lower still, 65–75%, because the scatter has to fit under the bolt’s limit: at ±30% a 75% target reaches 98% of proof at the top of the band. Note that higher preload is usually better for everything except the bolt’s own margin — it raises the separation load, it raises the friction capacity of the joint in shear, and it usually improves fatigue life. The reason not to go higher is the scatter, not the principle.

Does this page cover hex key sizes or tap drill diameters?

No, deliberately. This site already has a hex key and hex socket size page and it is not duplicated here. Tap drill and clearance-hole drill sizes, and pitch to threads per inch with the coarse and fine series, belong to the converters plugin. The line this project draws is that a drill or a size conversion is a converter, and a feature or a force on the part is mechanical. A tightening torque is a force question, so it lives here.

Related calculators

References

VDI 2230 Blatt 1, Systematic calculation of highly stressed bolted joints — Joints with one cylindrical bolt. Cited by clause and table; the guideline is copyrighted and was not reproduced. The tightening-torque terms used here are its own form, M_A = F_M[0.16 P + 0.58 d₂ μ_G + 0.5 D_Km μ_K], where the 0.58 is 0.5/cos 30° written out. Table A8 gives the tightening factor α_A; clause R12 gives the endurance limit; clause R4 gives the embedding amount f_Z.
VDI 2230 Blatt 1 Table A8 (“Guide values for the tightening factor α_A”), from the extract published by pvp-software.de. Thirteen tightening techniques with their α_A ranges, their setting technique and the ± scatter each implies. That scatter column is not independent data: it is exactly (α_A − 1)/(α_A + 1) rounded to a whole percent, at every one of the thirteen rows, which is what confirmed the column mapping of the extract before any of it was used.
Nord-Lock Group. What Is the Relationship Between Torque, Preload and Friction? The source for the torque split: “the breakdown of torque usually shows that only 10% of the input torque is useful”, with “underhead torque represents 50% of the input torque” and “thread torque is 40%”. This page does not take those three numbers on trust — it computes the three terms from the thread geometry and the bearing-face geometry and shows that they land on 12 / 40 / 48 percent for an M10 at a friction coefficient of 0.15, which is the same answer.
Portland Bolt. Bolt Torque Chart and Tension vs. Torque. Source for the other three nut factors: “waxed (e.g. pressure wax as supplied on high strength nuts) = .10, hot dip galvanized = .25, and plain non-plated bolts (as received) = .20”, tension taken at 75% of proof load. It also states the range plainly: K “can range from 0.10 for a well lubricated/waxed assembly, to over 0.30 for one that is dirty or rusty”, and that torque values “that claim to relate torque to pretension without verification shall not be used”.
Fastenal. Torque-Tension Reference Guide. Source for four of the published nut factors: 0.12 for a PTFE-type coating on nut, bolt and washer, 0.15 for lubricated conditions including oil and tapping fluid, 0.17 for some anti-seize, thread lockers and some plain conditions, and 0.20 for “zinc and dry conditions”. It states the target clamp load as “75% of the proof loads specified by the standard” and warns that “torque is only an indirect indication of tension”.
NASA Fastener Design Manual (RP-1228), as reproduced by the Engineering Library. Source for the torque coefficient table against equal thread and head friction — K = 0.074, 0.133, 0.189 and 0.250 at μ = 0.05, 0.10, 0.15 and 0.20 — and for the two accuracy tables: the Industrial Fasteners Institute’s (feel ±35%, torque wrench ±25%, turn of the nut ±15%, load-indicating washers ±10%, fastener elongation ±3 to 5%, strain gauges ±1%) and Machine Design’s control accuracies (torque ±15 to 30%, turn ±15 to 30%, torque and turn ±10 to 25%, torque past yield ±3 to 10%, bolt stretch ±1 to 8%).
Sandia National Laboratories, SAND2008-0371, Guideline for Bolted Joint Design and Analysis: Version 1.0, as reproduced by the Engineering Library. Source for the target preload rule, attributed there to Machinery’s Handbook: “use 75% of the proof strength … for removable fasteners and 90% of the proof strength for permanent fasteners”; for the torque-wrench accuracies by lubrication state (unlubricated ±35%, cadmium plated ±30%, lubricated ±25%); and for Shigley’s frustum form of the member stiffness with the statement that the cone half-angle “should be between 25 and 33 degrees and in general recommends 30 degrees”.
ISO 898-1:2013, Mechanical properties of fasteners made of carbon steel and alloy steel — Part 1: Bolts, screws and studs with specified property classes. Cited by clause; the standard is copyrighted and was not fetched. Clause 9.1.6.1 defines the nominal stress area as the circle on the mean of the pitch diameter d₂ and the minor diameter d₃ of the basic profile, which is where the 0.938194 on this page comes from — it is derived here from d₂ = d − 0.649519 P and d₃ = d − 1.226870 P, not copied. Table 3 carries the property classes.
Kova Fasteners. ISO 898 Part 1 – 2013 (Extract). The source for the minimum tensile strength R_m, the minimum yield or 0.2% proof strength, and the stress under proof load S_p for every property class used here. It also carries the note that for classes 4.8, 5.8 and 6.8 “the values for R_pf min are under investigation” — which is why the second digit of those three designations is a label and not a property.
SAE J429, Mechanical and Material Requirements for Externally Threaded Fasteners, as printed by STS Industrial and by Portland Bolt. The two size bands matter and two other transcriptions of this table lost them: one repeated grade 2’s 55/57/74 ksi row into the over-3/4-inch band, which is really 33/36/60, and another swapped grade 5’s large-size yield and tensile columns to give a yield above the tensile. The rule that a yield minimum cannot exceed a tensile minimum is what caught both.
ISO 3506-1:2020, Fasteners — Mechanical properties of corrosion-resistant stainless steel fasteners — Part 1: Bolts, screws and studs with specified grades and property classes, Table 2. Read from the copy hosted by fpg-co.com. Property class 50 is 500 N/mm² tensile and 210 N/mm² at 0.2% non-proportional elongation, class 70 is 700 and 450, class 80 is 800 and 600, and class 100 is 1,000 and 800. Note what is NOT in that table: a stress under proof load. ISO 3506 does not define one, so “75% of proof” has no meaning for a stainless bolt.