Bolt Proof Load and Tensile Stress Area Calculator

The tensile stress area computed from ISO 898-1’s own definition — the circle on the mean of the pitch and minor diameters, which is where the 0.938194 comes from — and the proof, yield, ultimate, clamp and shear loads that follow, for the metric property classes, for SAE grades with their size bands, and for the stainless classes that have no proof load at all.

Last updated 24 Sep 2026

Proof load and stress area

Size and class → area, proof load and clamp load

Thread sizeThe metric stress area uses ISO 898-1’s 0.938194 and the inch one the Unified 0.974279. Both constants are derived on this page from the thread profile, and both reproduce their own published area tables.

Property class or gradeClass 8.8 and grade 9.8 change value above M16, and SAE grades 2 and 5 change above 3/4 in and 1 in. The page picks the band from the size you chose and reports which one.

Clamp load wanted, % of the proof stressThis is the number the torque page needs. 75% for a removable fastener, 90% for a permanent one.

Shear-to-tensile ratio to use0.60 is the Industrial Fastener Institute’s convention, and it IS a convention: no ASTM or ISO fastener standard specifies a shear strength at all. Von Mises would say 0.577; some codes work at 0.62 or lower.

Not a circuit: one thread in axial half-section on the left, with every RADIUS drawn to scale for the size you chose, and the same three circles concentrically on the right. Reading down from the top: the major diameter, the thread form, the pitch diameter d₂, the diameter the tensile stress area is drawn on, ISO 898-1's d₃, and the minor diameter d₁. The stress diameter sits exactly halfway between d₂ and d₃ — that IS the definition, and the dimension on the right measures it as a length: 0.469 P below the major radius, which is the 0.938194 P of diameter this page derives. Two things are deliberately not to scale and both matter. The PITCH is exaggerated about sixfold, because a real 1.5 mm pitch beside a 10 mm diameter is a hairline. And the radial axis is a magnified WINDOW from 0.75 d to the full diameter rather than the whole radius — the hatched break at the bottom is where the rest of the bolt would be — because every diameter this page is about lives in the outer quarter and the core between them is empty — so the thread form is a schematic: its flanks on the page are much steeper than the real 60 degrees, because the radial axis is about three times the axial one. The circles on the right are to their own single scale and show the same thing as areas: the plain shank outside, the stress area at 68 to 82 per cent of it, and the minor-diameter circle at the thread root.

57.99mm²Example

M10 class 8.8, clamp load wanted at 75% of the proof stress

One area, three strengths, and the loads they give

A_s = (π/4)·[(d₂ + d₃)/2]² = (π/4)(d − 0.938194 P)² · d₂ = d − 0.649519 P · d₃ = d − 1.082532 P − H/6 · F_proof = A_s S_p · F_clamp = (pct/100) A_s S_p · F_shear ≈ 0.60 A_s R_m (a convention)

A_s: tensile stress area. Not the shank area and not the minor-diameter area: the circle on the mean of the pitch and minor diameters of the basic profile, which is 0.68 to 0.82 of the shank
H: height of the fundamental triangle, (√3/2)P. Every thread dimension on this page is a multiple of it
S_p: stress under proof load. A specified property in ISO 898-1 and SAE J429, and absent from ISO 3506 — stainless has no proof load
R_m: minimum tensile strength. For classes 10.9 and 12.9 it is ABOVE the nominal figure the designation gives
R_p0.2: 0.2% proof strength, the yield of a material with no sharp yield point. Also above the designation’s figure for 10.9 and 12.9, and unspecified for 4.8, 5.8 and 6.8
0.60: the shear-to-tensile convention. The Industrial Fastener Institute’s figure, and a convention rather than a property: no ASTM or ISO fastener standard specifies a shear strength

Worked example

M10 class 8.8, clamp load wanted at 75% of the proof stress
H = (√3/2) × 1.5 = 1.29904 mm. d₂ = 10 − 0.649519 × 1.5 = 9.0257 mm. d₁ = 10 − 1.082532 × 1.5 = 8.3762 mm, and d₃ = d₁ − H/6 = 8.1597 mm
Their mean is 8.5927 mm, which is 10 − 0.938194 × 1.5. That is where the constant comes from — it is not a fitted number
A_s = (π/4) × 8.5927² = 57.99 mm². The published ISO 898-1 column says 58.0. The shank is 78.54 mm², so A_s is 0.738 of it
Class 8.8 at M10 is in the d ≤ 16 band: R_m min 800, R_p0.2 min 640, S_p 580 N/mm². Check the designation: 8 × 100 = 800 ✓ and 8 × 8 × 10 = 640 ✓
Proof load = 57.99 × 580 = 33.63 kN. It yields at 37.11 kN and breaks at 46.39 kN. Note how close the proof load is to yield: 580/640 = 0.906, so proof load is not a comfortable working load, it is a not-quite-yield load
Clamp load at 75% of proof = 25.23 kN, which is the figure the bolt torque calculator turns into a torque
Shear: 0.60 × 800 = 480 N/mm² on the stress area is 27.84 kN, or 37.7 kN if the shear plane misses the thread and lands on the shank. Both of those are conventions on a strength no standard specifies

The stress area computed from the definition, against the published column

Nothing in the A_s column was copied. ISO 898-1 defines the stress area as the circle on the mean of the pitch diameter d₂ and the minor diameter d₃ of the basic profile. From ISO 68-1, d₂ = d − 0.649519 P and d₁ = d − 1.082532 P; ISO 898-1 sets d₃ = d₁ − H/6 where H = 0.866025 P, giving d₃ = d − 1.226870 P. The mean of those two coefficients is 0.938194, and that is where the constant comes from — it is half the sum of two numbers that are themselves 3/4 and 5/4 of the fundamental triangle height plus a sixth of it. The computed column reproduces the published one at all fifteen sizes to better than 0.4%, which is the rounding in a three-figure table. The last column is worth remembering: A_s is 0.68 to 0.82 of the shank area, which is why AISC’s knock-down for threads in the shear plane is 0.80. 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.
Size	Pitch P (mm)	d₂ (mm)	d₃ (mm)	(d₂+d₃)/2 (mm)	A_s computed (mm²)	A_s published (mm²)	A_s ÷ shank area
M4	0.70	3.545	3.141	3.343	8.78	8.8	0.6986
M5	0.80	4.480	4.019	4.249	14.18	14.2	0.7223
M6	1.00	5.350	4.773	5.062	20.12	20.1	0.7117
M8	1.25	7.188	6.466	6.827	36.61	36.6	0.7283
M10	1.50	9.026	8.160	8.593	57.99	58.0	0.7383
M12	1.75	10.863	9.853	10.358	84.27	84.3	0.7451
M14	2.00	12.701	11.546	12.124	115.44	115.0	0.7499
M16	2.00	14.701	13.546	14.124	156.67	157.0	0.7792
M18	2.50	16.376	14.933	15.655	192.47	192.0	0.7564
M20	2.50	18.376	16.933	17.655	244.79	245.0	0.7792
M22	2.50	20.376	18.933	19.655	303.40	303.0	0.7981
M24	3.00	22.051	20.319	21.185	352.50	353.0	0.7792
M27	3.00	25.051	23.319	24.185	459.41	459.0	0.8024
M30	3.50	27.727	25.706	26.716	560.59	561.0	0.7931
M36	4.00	33.402	31.093	32.247	816.72	817.0	0.8024

ISO 898-1: the designation rule, and the three places it stops being arithmetic

The rule everybody learns is right and incomplete. The first digit × 100 is the nominal tensile strength, and the two digits multiplied × 10 is the nominal yield: 8.8 means 800 and 640. Read the last column and see where it stops. For classes 10.9 and 12.9 the SPECIFIED minimum yield is 940 and 1,100, not the 900 and 1,080 the designation gives, and their specified minimum tensile strengths are 1,040 and 1,220, not 1,000 and 1,200 — which is a disagreement between publishers as well as between the rule and the standard: RoyMech print 1,000 and 1,200, where Kova and Fastenal print the standard’s figures. Class 8.8 changes value at M16, so the same designation has two sets of numbers. And for classes 4.8, 5.8 and 6.8 there is no specified minimum yield at all — Kova’s extract carries the note that “the values for R_pf min are under investigation” — so for those three the second digit is a label and not a property you can design to. 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.
Class	Nominal Rₘ from the first digit	Specified minimum Rₘ	Nominal yield from the two digits	Specified minimum yield	Stress under proof load S_p	Specified minus nominal yield
4.6	400	400	240	240	225	same
4.8	400	420	320	—	310	not specified
5.6	500	500	300	300	280	same
5.8	500	520	400	—	380	not specified
6.8	600	600	480	—	440	not specified
8.8 (d ≤ 16)	800	800	640	640	580	same
8.8 (d > 16)	800	830	640	660	600	+20
9.8 (d ≤ 16)	900	900	720	720	650	same
10.9	1,000	1,040	900	940	830	+40
12.9	1,200	1,220	1,080	1,100	970	+20

SAE J429, and the metric class each grade really sits next to

Grade 5 at 120 ksi is 827 N/mm², so it is very close to a class 8.8 — that is the comparison people want and it is close enough to be useful. Grade 8 at 150 ksi is 1,034 N/mm², which sits between class 9.8 and class 10.9 and is NOT a 10.9. Note the size bands: grade 2 above 3/4 in has grade 1’s strengths, and grade 5 above 1 in drops from 120 to 105 ksi. Those bands are the rows transcriptions lose. Two of the copies of this table this batch fetched were wrong — one repeated grade 2’s small-size row into the large-size band and one swapped grade 5’s large-size yield and tensile columns, giving a yield above the tensile — and the rule that a yield minimum cannot exceed a tensile minimum is what caught both. 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.
Grade and size band	Proof load stress (ksi)	Min yield (ksi)	Min tensile (ksi)	Proof (N/mm²)	Yield (N/mm²)	Tensile (N/mm²)	Yield ÷ tensile
SAE grade 1	33	36	60	228	248	414	0.600
SAE grade 2, ≤ 3/4 in	55	57	74	379	393	510	0.770
SAE grade 2, > 3/4 in	33	36	60	228	248	414	0.600
SAE grade 5, ≤ 1 in	85	92	120	586	634	827	0.767
SAE grade 5, > 1 in	74	81	105	510	558	724	0.771
SAE grade 8	120	130	150	827	896	1,034	0.867

Stainless is not high strength, and it has no proof load

A2-70 is the stainless bolt most people mean when they say “stainless”, and at 700 N/mm² it is weaker than a class 8.8 at 800 and barely half a class 12.9. A4-80 at 800 matches an 8.8 and no more. The other column matters more than it looks: ISO 3506-1 Table 2 specifies a tensile strength and a stress at 0.2% non-proportional elongation, and nothing else. There is no stress under proof load, so “torque to 75% of proof” has no referent for a stainless bolt and this page uses the 0.2% proof strength as the reference instead. Two more practical points: the yield ratio is 0.64 rather than the 0.8 a carbon-steel class gives, so a stainless bolt yields proportionally earlier; and austenitic stainless galls against itself, which puts the thread friction — and therefore the nut factor on the bolt torque calculator — far above the usual assumption unless the thread is lubricated. 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.
ISO 3506-1 class	Min tensile Rₘ (N/mm²)	0.2% proof R_p0.2 (N/mm²)	Ratio	Stress under proof load	Load at 0.2% proof on an M10 (kN)
A2-50 / A4-50 (soft, class 50)	500	210	0.420	none — ISO 3506 does not define one	12.18
A2-70 / A4-70 (class 70)	700	450	0.643	none — ISO 3506 does not define one	26.10
A4-80 / A2-80 (class 80)	800	600	0.750	none — ISO 3506 does not define one	34.79
A4-100 (class 100)	1,000	800	0.800	none — ISO 3506 does not define one	46.39

Why the inch constant is 0.9743 and not 0.9382

Both families take the pitch diameter and shrink the RADIUS, and they shrink it by different amounts. The metric convention takes off H/6 and the Unified one takes off 3H/16 — a ratio of exactly 9/8 — so the diameter coefficients come out at 0.649519 + 2(H/6)/P = 0.938194 and 0.649519 + 2(3H/16)/P = 0.974279. The last column shows what using the wrong one costs: about 1% of area on a 1/4 in and 0.3% on a 1 in, which is small but is not nothing, and it is the kind of error that hides forever. Both computed columns reproduce their own published tables to better than 0.4%. 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.
Size	Threads per inch	Pitch (in)	A_s computed (in²)	A_s published (in²)	A_s (mm²)	What the METRIC constant would have given (in²)
1/4-20	20	0.05000	0.03182	0.0318	20.53	0.03239
5/16-18	18	0.05556	0.05243	0.0524	33.83	0.05325
3/8-16	16	0.06250	0.07749	0.0775	49.99	0.07861
7/16-14	14	0.07143	0.10631	0.1063	68.59	0.10780
1/2-13	13	0.07692	0.14190	0.1419	91.55	0.14376
5/8-11	11	0.09091	0.22600	0.2260	145.81	0.22878
3/4-10	10	0.10000	0.33446	0.3345	215.78	0.33817
7/8-9	9	0.11111	0.46174	0.4617	297.89	0.46658
1-8	8	0.12500	0.60575	0.6057	390.80	0.61199

Where 0.938194 comes from, and the three places the property class rule stops

The tensile stress area is the one number every other bolt calculation needs, and it is not the area of anything you can measure directly. It is not the shank, which is 20–30% bigger. It is not the minor-diameter circle at the thread root, which is a few per cent bigger. ISO 898-1 defines it as the circle drawn on the mean of the pitch diameter d₂ and a diameter d₃ that is the basic minor diameter less a sixth of the fundamental triangle height. Work that through and the familiar constant appears: d₂ = d − 0.649519P, d₃ = d − 1.226870P, and their mean is d − 0.938194P. The 0.938194 is not a fitted number and not a measurement — it is half the sum of two thread-geometry coefficients, and this page shows the sum.

The inch constant is different, and the reason is worth knowing. A Unified thread’s stress area uses (π/4)(D − 0.9743/n)². Same 60° thread, same pitch diameter, different constant — because the two conventions shrink the pitch radius by different amounts. Metric takes off H/6; Unified takes off 3H/16, which is exactly 9/8 of it. Both computed columns on this page reproduce their own published area tables to better than 0.4%, and the table shows what applying the wrong constant costs: about 1% of area on a 1/4 in bolt.

The property class rule works, and then it stops working in three places. First digit × 100 is the nominal tensile strength; the two digits multiplied × 10 is the nominal yield. 8.8 is 800 and 640, and that is exactly what ISO 898-1 specifies. But for class 10.9 the standard specifies minima of 1,040 and 940 where the designation says 1,000 and 900, and for 12.9 it specifies 1,220 and 1,100 where the designation says 1,200 and 1,080. Class 8.8 changes value above M16. And for classes 4.8, 5.8 and 6.8 there is no specified minimum yield at all — the standard records that the values are under investigation — so for those three the second digit is a label. Publishers disagree about the first of those: RoyMech’s widely-copied table prints the nominal values for 10.9 and 12.9 as though they were the minima. Four per cent of capacity hangs on which table you read.

Shear strength is not a specified property of any fastener, in any standard. The Industrial Fastener Institute’s convention, quoted by Portland Bolt, is that “shear strength is approximately 60 percent of the minimum tensile strength”, with the explicit note that “there are no published shear strength values or requirements for ASTM specifications”. Von Mises would say 0.577 for a ductile material. AISC works at 0.450 and 0.563 of the tensile strength depending on whether the thread is in the shear plane. This page prints the convention, lets you change it, and says which it is — because the honest answer to “what is the shear strength of a grade 8 bolt?” begins with “nobody specifies one”.

And stainless is not the strong option. ISO 3506-1 puts A2-70 at 700 N/mm² tensile and 450 at 0.2% proof: weaker than a class 8.8 on both counts, and a little over a third of a 12.9 on yield. It also specifies no stress under proof load at all, so the usual instruction to preload to 75% of proof has nothing to refer to. Use the 0.2% proof strength, say that you are doing so, and remember that austenitic stainless galls against itself, which moves the nut factor on the bolt torque calculator a long way from its usual value. From here, the clamp load goes to the torque page, the thread capacity to the thread engagement length calculator, and the scatter that determines how much of this capacity you can actually count on to the preload accuracy by tightening method calculator.

Frequently asked questions

Why is the tensile stress area smaller than the bolt’s cross-section?

Because the thread is cut into the bolt, so the load-carrying metal is inside the thread root, not out at the nominal diameter. ISO 898-1 takes the area of a circle on the mean of the pitch diameter and a diameter slightly below the basic minor diameter, which comes out at (π/4)(d − 0.938194P)². For an M10 that is 58.0 mm² against a shank of 78.5 mm² — 74% of it. Across the metric coarse series the ratio runs from 0.68 to 0.82, rising with diameter because the pitch grows more slowly than the diameter does.

What is proof load, and is it a safe working load?

Proof load is the tensile load a bolt must carry without any measurable permanent set. It is a test requirement, not a working load, and it is close to yield: for a class 8.8 the proof stress is 580 N/mm² against a minimum 0.2% proof strength of 640, so proof load is 91% of yield. That is exactly why preload targets are quoted as percentages OF proof load — 75% for a removable fastener and 90% for a permanent one, per Machinery’s Handbook. And it is why the scatter in tightening matters so much: a 75% target with ±30% scatter reaches 98% of proof at the top of the band.

What does 8.8 actually mean?

The first digit is the nominal tensile strength in hundreds of newtons per square millimetre, so 8 means 800. The second digit is ten times the ratio of yield to tensile, so 8 means 0.8 and the nominal yield is 640. RoyMech state it cleanly: the second number is the ratio of the proof or yield stress to the tensile strength as a percentage, divided by 100. The rule is exact for the NOMINAL values. It is not exact for what ISO 898-1 specifies: 10.9 and 12.9 both have specified minima above what the digits give, class 8.8 changes above M16, and classes 4.8, 5.8 and 6.8 have no specified yield minimum at all.

Is a grade 8 bolt the same as a class 10.9?

No. SAE grade 8 is 150 ksi minimum tensile, which is 1,034 N/mm² — above class 9.8’s 900 and below class 10.9’s specified 1,040. Its yield is 130 ksi, 896 N/mm², against 10.9’s 940. So grade 8 is a little weaker than 10.9 and a lot stronger than 8.8. The closer equivalence is grade 5 to class 8.8: 120 ksi is 827 N/mm² against 800, and 92 ksi yield is 634 against 640. Neither pairing is a substitution you should make on a drawing without checking the thread series and the marking requirements too.

What is the shear strength of a bolt?

No fastener standard specifies one. The convention, from the Industrial Fastener Institute’s Inch Fastener Standards and quoted by Portland Bolt, is 60% of the minimum tensile strength, so a grade 5 at 120 ksi is taken as 70 ksi in shear. This page computes that on the tensile stress area and also on the plain shank, because whether the shear plane lands on the thread makes a real difference — AISC handles the same point with two different allowable stresses, 0.450 and 0.563 of the tensile strength, whose ratio of 0.80 is close to the stress-area-to-shank ratio. If the answer matters structurally, use the code’s numbers and not this convention; the bolt group shear calculator does the code checks.

Why is my stainless bolt weaker than a plain steel one?

Because it is. A2-70 is 700 N/mm² minimum tensile and 450 at 0.2% proof; a class 8.8 is 800 and 640. A4-80 gets you to 800 tensile and 600 proof, which still does not match an 8.8’s yield. Austenitic stainless cannot be quench-and-temper hardened the way a class 10.9 alloy steel is; the strength comes from cold work, which is why class 50 exists for the annealed condition at 500 and 210. Stainless is a corrosion decision. If you need strength and corrosion resistance together, that is a coating or a duplex or precipitation hardening grade, not an A2.

Related calculators

References

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.
RoyMech. Metric Bolt Strength Chart (ISO 898-1). Used as the cross-check on the property classes, and it disagrees on two rows: it prints the minimum tensile strength of classes 10.9 and 12.9 as 1,000 and 1,200 N/mm², which are the NOMINAL values. ISO 898-1 specifies 1,040 and 1,220; Fastenal and Kova both print those. RoyMech’s own statement of the designation rule is quoted on this page because it is the clearest one found: the second number is “the ratio of the Proof (or Yield) stress and the Tensile strength expressed as a percentage”, divided by 100.
Fastenal Engineering & Design Support. Mechanical Properties Per ISO 898-1 (Externally Threaded Fasteners) and the Torque-Tension Charts for Metric Fasteners. Source for the published tensile stress area column that the ISO 898-1 formula was checked against at all fifteen metric sizes, and for the minimum tensile strengths of classes 10.9 (1,040 N/mm²) and 12.9 (1,220 N/mm²). Its own property-class table was read through a summariser that shifted a column — it returned class 8.8 as “min tensile 640, min proof 240”, which are the 8.8 yield and the 4.6 proof stress — so only the figures a second source confirmed are used.
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.
Portland Bolt. Bolt Shear Strength Considerations. The source for the shear convention, attributed there to the Industrial Fastener Institute’s Inch Fastener Standards, 7th ed. 2003, B-8: “shear strength is approximately 60 percent of the minimum tensile strength”, with the caveat that “unlike tensile and yield strengths, there are no published shear strength values or requirements for ASTM specifications”. It is a convention, not a specified property.
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”.
RoyMech. Screw Thread Stress Area Calculations. The source for the published simplified engagement-length method, Lₑ = 2Aₜ / (0.5π d₂), and for the worked M6 case it reproduces. Its printed stress-area formula and its printed stress-area NUMBER disagree — the formula as transcribed carries 0.64952 where the quoted 20.1234 mm² for M6 can only come from 0.938194 — so the number was believed and the transcription was not.