Spring Wire Material and Allowable Stress Calculator

S_ut = A/d^m computed for seven spring wires, with the allowable stress for the material, the wire diameter and the service you name — plus both moduli per material, the temperature limits, and a refusal where the honest answer is not a percentage.

Last updated 24 Sep 2026

Spring wire strength and allowable stress

Material, diameter, service → strength and allowable

Wire materialSeven of the wires spring makers actually stock. Each one carries its own A and m constants, its own two moduli and its own temperature limit, and none of those is interchangeable with another’s.

Wire diameter d (mm)THE POINT OF THIS PAGE. Tensile strength falls as diameter rises, because a thicker wire has had less cold work drawn into it. Over music wire’s full range the strength falls about 30 per cent; over 302 stainless’s, nearly half.

What the spring isThe allowable is a percentage of tensile strength and the percentage depends on how the wire is loaded, not only on what it is. Torsion for a coil body, bending for a torsion spring or a hook, and a lower figure again for a hook in torsion.

DutyStatic means loaded a few thousand times at most. If the spring is cycled, no percentage of tensile strength is the right answer and this page will say so rather than give you one.

Spring index C = D/d, for the load conversionOnly used to turn the allowable stress into a force or a torque. The stress itself does not depend on it; the correction factor does.

Service temperature (°C)Compared against the material’s published maximum. Note that SET — a permanent loss of free length — begins well below any temperature at which the material would yield, and well below these limits for a highly stressed spring.

Not a circuit: minimum tensile strength against wire diameter, on a logarithmic diameter axis, for three of the seven materials. Each line is S_ut = A/d^m over the diameter range that material is actually specified in, so a line that stops has run out of specification rather than out of chart. Three things to read. The lines do not all stay in the same order. Music wire is above both the others at every diameter it is made in, which is why it is the wire everything else is priced against. The SLOPES differ, and that matters more than the offsets: hard-drawn falls off at m = 0.19 against music wire's 0.145, so the gap between them widens as the wire gets thicker. And the other two lines DO cross, at about 5.5 mm — 302 stainless is stronger than hard-drawn wire in fine sizes and weaker in heavy ones, because its published fit steepens to m = 0.478 above 5 mm. The stainless line's visible kinks at 2.5 and 5 mm are that same three-band fit showing; they are real data, not an artefact. The moving vertical is your own diameter, in forty steps across two decades.

2,000MPaExample

ASTM A228 music wire, 2 mm diameter, in a compression spring body under static load at room temperature

Strength from diameter, allowable from service

S_ut = A/d^m · τ_allow = (percentage)·S_ut · F_max = τ_allow·πd³/(8·D·K_W) · M_max = σ_allow·πd³/(32·K_i)

A, m: published constants per material and per diameter band. A is in MPa·mm^m, so the units only work with d in millimetres — the inch-pound constants are entirely different numbers
S_ut: MINIMUM tensile strength, not typical. The fit lands near the bottom of the published band, which is the direction a design wants
the percentage: the published allowable as a fraction of minimum tensile. Depends on the material AND on how the wire is loaded: about 45 per cent in torsion, about 75 in bending, 40 for a hook in torsion, and 35 in torsion for stainless and non-ferrous
G: shear modulus — sets the rate of a compression or extension spring. 79.3 GPa for carbon steel wire, 69 for 302 stainless, 41.4 for phosphor bronze
E: Young’s modulus — sets the rate of a torsion spring, whose wire is in bending. E/G is about 2.6 for steel and 2.5 for bronze
F_max, M_max: what the allowable means in the units you can measure: the force a coil of this wire at this index may carry, or the torque if it is loaded in bending

Worked example

ASTM A228 music wire, 2 mm diameter, in a compression spring body under static load at room temperature
Strength first, and the point of the page is that it depends on the diameter. Music wire's published constants are A = 2,211 MPa·mm^m and m = 0.145, over 0.1 to 6.5 mm, so S_ut = A/d^m = 2,211/2^0.145 = 2,211/1.105731 = 2,000 MPa
Check the gradient, because it is the reason this is a formula and not a single number. The same wire at 0.1 mm is 3,087 MPa and at 6.5 mm it is 1,685 MPa — a fall of 45 per cent across the range it is made in. Doubling YOUR wire to 4 mm would cost 9.6 per cent of the strength
AND THIS IS VERIFIED, NOT QUOTED. Suhm Spring Works publishes a minimum-tensile column for A228 against diameter in inches. At 0.012 in this fit gives 381 ksi against a printed 377–417; at 0.100 in it gives 280 against 271–300; at 0.250 in it gives 245 against 230–255. Six diameters over a 20:1 range, all within three per cent of the published minimum
Now the allowable, which needs THREE things and not one: the material, the wire diameter, and what the spring is. For a compression spring body under static load Shigley's Table 10-6 gives 45 per cent of minimum tensile for music wire, so τ_allow = 0.45 × 2,000 = 900 MPa
Put it in units you can use. At a spring index of 7 the Wahl factor is 1.2129, so the largest force this wire may carry in such a coil is F = τπd³/(8DK_W) = 166.5 N. That is a number you can compare with a load
THE THREE THINGS THAT WOULD CHANGE THAT ANSWER. Swap to 302 stainless and the tensile at 2 mm becomes 1,687 MPa, the percentage drops to 35, and the allowable becomes 591 MPa — 34 per cent less. Swap to phosphor bronze and it becomes 313 MPa, less than a third. Keep the material and make it a TORSION spring instead and the wire is in bending, where the allowable is about 75 per cent, so it RISES to 1,500 MPa
The moduli, which is the other half of a material decision. Music wire is G = 79.3 and E = 206.8 GPa. 302 stainless is G = 69 and E = 193, so a stainless spring of identical geometry is 13 per cent softer in compression and 7 per cent softer in torsion — DIFFERENT amounts, because E/G is not the same for the two materials. Phosphor bronze is G = 41.4, nearly half
Temperature, and a refusal. Music wire's published limit is 121 °C (250 °F). Above it the modulus falls and the spring relaxes, and SET — a permanent loss of free length — begins well below any temperature at which the material would yield and well below this limit for a highly stressed spring. This page will not put a number on the modulus loss with temperature, because the published data is per grade and per stress level and there is no honest general curve. Neither will it give you a fatigue allowable as a percentage of tensile: that needs an endurance amplitude and a mean-stress rule, not a fraction

S_ut = A/d^m — computed, not tabulated

Tensile strength is a function of diameter because strength in cold-drawn wire comes from the drawing, and a thicker wire has had proportionally less of it. The published form is S_ut = A/d^m, and these are the SI constants from Shigley’s Table 10-4, cross-checked row for row against RoyMech’s independent printing. They are USED rather than reproduced: the page computes the strength at your diameter. The check that makes them trustworthy is Suhm Spring Works’ published minimum-tensile column for music wire: at 0.012, 0.025, 0.050, 0.100, 0.177 and 0.250 inches this fit lands within three per cent of the printed minimum, over a 20:1 diameter range, and the three-band 302 stainless fit lands within two per cent at four diameters. NOTE that Juvinall and Marshek publish DIFFERENT constants for the same wires — 2,170 and 0.146 for music wire against 2,211 and 0.145, 1,750 and 0.192 for hard-drawn against 1,783 and 0.190. The difference is under two per cent and neither is a misprint; they are two fits to overlapping data. 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.
Material	ASTM	A (MPa·mm^m)	m	Diameter range (mm)	S_ut at 1 mm	S_ut at 3 mm
Music wire	ASTM A228	2,211	0.145	0.10–6.50	2,211	1,885
Hard-drawn wire	ASTM A227	1,783	0.190	0.70–12.70	1,783	1,447
Oil-tempered wire	ASTM A229	1,855	0.187	0.50–12.70	1,855	1,511
Chrome silicon	ASTM A401	1,974	0.108	1.60–9.50	1,974	1,753
Chrome vanadium	ASTM A232	2,005	0.168	0.80–11.10	2,005	1,667
302 stainless	ASTM A313	1,867 / 2,065 / 2,911	0.146 / 0.263 / 0.478	0.30–2.50 / 2.50–5.00 / 5.00–10.00	1,867	1,547
Phosphor bronze	ASTM B159	1,000 / 913 / 932	0.000 / 0.028 / 0.064	0.10–0.60 / 0.60–2.00 / 2.00–7.50	913	869

The allowable is a percentage of tensile, and three sources publish three sets

This is the number most likely to be quoted wrongly, and the honest answer is that there is more than one published figure for most of these wires. Shigley’s Table 10-6 gives 45 per cent of minimum tensile in torsion for music wire and hard-drawn, 50 for oil-tempered and the alloy steels, and 35 for austenitic stainless and non-ferrous. Victory Spring’s *Comprehensive Spring Design* gives 40 per cent for hard-drawn and for A313 stainless and 45 for the rest. Century Spring’s extension spring guide gives a BAND of 30 to 45 per cent for an extension body and 75 per cent in bending for a hook. Where they disagree, this page prints both and names both. And RoyMech’s own published position deserves quoting because it is the most careful of the four: “do not use a fixed percentage of tensile strength as a universal spring allowable”. Note too that the BENDING allowable is HIGHER than the torsional one — about 75 per cent against 45 — because bending strength exceeds shear strength, so a torsion spring is allowed more of its material’s tensile than a compression spring is, not less. 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. 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.
Material	Torsional, static — Shigley Table 10-6	… the more conservative reading	Extension hook in torsion	Bending, static	Torsional allowable at 2 mm (MPa)	Bending allowable at 2 mm (MPa)
Music wire	45 %	45 %	40 %	75 %	900	1,500
Hard-drawn wire	45 %	40 %	40 %	75 %	703	1,172
Oil-tempered wire	50 %	45 %	40 %	75 %	815	1,222
Chrome silicon	50 %	45 %	40 %	75 %	916	1,374
Chrome vanadium	50 %	45 %	40 %	75 %	892	1,338
302 stainless	35 %	40 %	40 %	55 %	591	928
Phosphor bronze	35 %	35 %	40 %	55 %	313	492

Both moduli and the temperature limit, per material — with the second published value where the sources disagree

A page that uses 79.3 GPa for every spring is wrong for two of these seven and badly wrong for one. 302 stainless is 69 GPa, so an identical spring in stainless is 13 per cent softer than in carbon steel; phosphor bronze is 41.4, nearly half. Carry the right one or the rate is out by more than any manufacturing tolerance. The E/G column matters too, because it is the ratio between how a material behaves in a compression spring and in a torsion spring: swap material and the two do not move by the same factor. The second-value columns are real disagreements between named sources, not uncertainty bars: Suhm Spring Works prints 9.8 Mpsi for 302 stainless where Master Spring prints 10.0, and 250 °F for oil-tempered wire and 500 °F for 302 stainless where Master Spring prints 300 and 600. Shigley gives the alloy steels E = 203.4 and G = 77.2 GPa where both catalogues give 206.8 and 79.3. None of these is large, and printing one without saying it is one of two is what makes a page look more certain than it is. 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.
Material	E (GPa)	Second published E	G (GPa)	Second published G	E/G	Max service temperature	Second published limit
Music wire	206.8	—	79.3	—	2.608	121 °C (250 °F)	—
Hard-drawn wire	206.8	—	79.3	—	2.608	121 °C (250 °F)	—
Oil-tempered wire	206.8	—	79.3	—	2.608	149 °C (300 °F)	121 °C
Chrome silicon	203.4	206.8	77.2	79.3	2.635	246 °C (475 °F)	—
Chrome vanadium	203.4	206.8	77.2	79.3	2.635	218 °C (425 °F)	—
302 stainless	193.0	—	69.0	67.6	2.797	260 °C (500 °F)	316 °C
Phosphor bronze	103.4	—	41.4	43.1	2.498	93 °C (200 °F)	—

Strength falls with diameter, the allowable needs three inputs, and two things this page will not tell you

Tensile strength is a function of wire diameter, and it is a big function. Strength in cold-drawn spring wire comes from the drawing itself, and a thicker wire has had proportionally less of it, so the published relation is S_ut = A/d^m with A and m tabulated per material. Music wire falls from 3,087 MPa at 0.1 mm to 1,685 MPa at 6.5 mm, a loss of 45 per cent across the range it is made in; 302 stainless falls by nearly half. That is far too much to fold into a single number, which is why this page computes rather than tabulates. The fit is checked rather than quoted: it reproduces Suhm Spring Works’ published minimum-tensile column for music wire within three per cent at six diameters over a 20:1 range, and 302 stainless’s three-band fit within two per cent at four.

The allowable needs three inputs, not one. It is a percentage of minimum tensile strength, and the percentage depends on the material AND on how the wire is loaded AND on the service. A compression spring body in torsion gets about 45 per cent for carbon steel wire and 35 for stainless and non-ferrous. An extension spring’s hook in torsion gets 40. Anything in BENDING — a torsion spring, or an extension spring’s loop bend — gets about 75 per cent, which is HIGHER, because bending strength exceeds shear strength in a ductile metal. That last point is worth stating plainly because the opposite is often claimed. And three published sources give three different sets of percentages for the same wires; where they disagree this page prints both and names both.

G and E both differ by material, and they differ by different amounts. A page that uses 79.3 GPa for everything is wrong for two of the seven wires here and badly wrong for one: 302 stainless is 69 GPa and phosphor bronze is 41.4. Since a compression spring’s rate is linear in G, a stainless spring of identical geometry is 13 per cent softer and a bronze one is nearly half as stiff. But a torsion spring’s rate is linear in E instead, and E/G is not constant across materials — so swapping material changes a compression spring and a torsion spring by DIFFERENT factors. This page carries both moduli for every wire, and the second published value where two named sources disagree, which they do for 302 stainless’s G, for phosphor bronze’s G and for the alloy steels’ E and G.

Temperature, and two refusals. Every spring material has a published maximum service temperature, from phosphor bronze’s 93 °C to 302 stainless’s 260, and this page compares yours against it. Above the limit two things happen: the modulus falls, which is recoverable, and the spring SETS — permanently loses free length — which is not. Set is a creep process, so it depends on stress and duration as well as temperature, and it begins well below any yield criterion. This page will NOT put a number on either effect, because the published data is per grade and per stress level and no honest general curve exists. Nor will it give a FATIGUE allowable as a percentage of tensile: for springs the endurance amplitude is nearly independent of wire size and tensile strength below about 10 mm, so a fraction of tensile is the wrong shape of answer entirely. Selecting a cycled duty on this page returns nothing and says why.

What is next door and is not here. Hardness conversion, surface roughness, density and wire gauge are all on this site’s converters, which are a separate family of pages from this one and are not linked from here — the link helper on these pages only builds mechanical URLs. If you need to turn a wire gauge into a diameter before using this page, or a Rockwell number into a tensile strength, look for the converter rather than expecting it here.

Frequently asked questions

Why does tensile strength depend on wire diameter?

Because in cold-drawn spring wire the strength comes from the drawing, and a thicker wire has had proportionally less reduction worked into it. The published relation is S_ut = A/d^m with A and m per material, and the effect is large: music wire loses about 30 per cent of its strength across the range it is made in, and 302 stainless nearly half. A single number for “the tensile strength of music wire” is meaningless without the diameter attached.

What percentage of tensile strength can I use?

It depends on the material, on whether the wire is in torsion or bending, and on the service, and there is more than one published answer. Shigley’s Table 10-6 gives 45 per cent in torsion for music wire and hard-drawn, 50 for oil-tempered and the alloy steels, 35 for stainless and non-ferrous. Victory Spring gives 40 for hard-drawn and stainless. Century Spring gives 30 to 45 as a band for extension spring bodies. In BENDING the figure is about 75 per cent, which is higher. This page prints the figure for your combination and the conservative alternative beside it.

Is the allowable for a torsion spring lower than for a compression spring?

For static loading, no — it is higher, and the opposite claim is common enough to be worth correcting. A torsion spring’s wire is in BENDING, and the published static allowable in bending is about 75 per cent of minimum tensile against 45 per cent in torsion, because bending strength exceeds shear strength in a ductile metal. What IS lower for a torsion spring is the fatigue allowable relative to the static one, which is a different comparison. Fatigue is not a percentage of tensile at all and this page will not pretend it is.

Can I use 79.3 GPa for G whatever the wire is?

No. It is right for carbon steel spring wire — music wire, hard-drawn, oil-tempered — and wrong for the rest. 302 stainless is 69 GPa, so a stainless spring of identical geometry is 13 per cent softer; phosphor bronze is 41.4, nearly half. And because a torsion spring’s rate depends on E rather than G, and E/G varies between materials, a material swap moves a compression spring and a torsion spring by different factors. Both moduli for all seven wires are on this page.

Why will this page not give me a fatigue allowable?

Because a fatigue allowable for a spring is not a percentage of tensile strength and cannot honestly be turned into one. It is an endurance amplitude at a given mean stress, and for springs the published data — Zimmerli’s, which Shigley uses — is nearly independent of wire size, material and tensile strength for wire under about 10 mm. Multiplying the static percentage by some fraction would be inventing data. What you actually need is the mean and alternating stress components, an endurance amplitude for the wire in its real surface condition, and a mean-stress rule such as Goodman.

What is ‘set’ and why does it happen below the temperature limit?

Set is a permanent loss of free length — the spring comes back shorter than it went in and never recovers. It is a creep process, so it depends on stress, temperature and time together, which is why it begins well below any temperature at which the material would yield and well below the catalogue’s maximum service temperature for a highly stressed spring. Deliberate pre-setting in manufacture exploits the same process to raise the usable stress; unintended set in service is the same thing happening when you did not want it.

Which of these wires should I default to?

Hard-drawn A227 for anything non-critical, because it is the cheapest; music wire A228 where the spring matters and the diameter is under 6.5 mm, because it is the strongest; oil-tempered A229 above that; chrome silicon A401 where the temperature is raised or the loading is shock; 302 stainless A313 where corrosion matters, accepting a 13 per cent softer spring and a lower allowable; and phosphor bronze only where you need conductivity or non-magnetic behaviour, because it is less than half as strong and less than half as stiff.

Related calculators

References

R. G. Budynas and J. K. Nisbett, Shigley’s Mechanical Engineering Design, chapter 10 “Mechanical Springs”. The source for the four-way end-condition table (Table 10-1, itself attributed there to Associated Spring’s Design Handbook), for the Bergsträsser factor, for the buckling constants C₁′ and C₂′, for the torsion-spring constant 10.8, and for the S_ut = A/d^m constants. Two of its published worked solutions (problems 10-35 and 10-37) were reproduced here to four significant figures as a check on the initial-tension band, and the end-condition table was checked cell for cell against RoyMech’s independent printing.
Suhm Spring Works, Spring Materials, Sizes & Strength Values, issue 10a. The published minimum and maximum tensile strength columns against wire diameter for ASTM A228 music wire and A313 type 302 stainless, the moduli E and G per material, and the maximum service temperatures. This is the catalogue the A/d^m fit was checked against at ten diameters over a 20:1 range; it is also the source of one of the two published temperature limits carried for oil-tempered wire and for 302 stainless.
Master Spring & Wire Form Co., Material Data and Torsion Spring Design. The second published modulus and maximum-temperature table, carried because it DISAGREES with Suhm’s on two rows — 300 °F against 250 °F for oil-tempered wire and 600 °F against 500 °F for type 302 stainless — and on the shear modulus of phosphor bronze (6.25 against 6.0 Mpsi). Both readings are printed on the wire page.
RoyMech, Helical Spring Design — Compression and Extension Springs and Spring Materials. Used as the independent check on the four-way end-condition table (which agrees with Shigley’s Table 10-1 cell for cell), on the SI A and m constants, and on the shear moduli. RoyMech’s own published position is worth quoting because it is the honest one: “do not use a fixed percentage of tensile strength as a universal spring allowable”.
Victory Spring / Comprehensive Spring Design, section 7. The third published set of allowables: 40 % of minimum tensile for hard-drawn A227 and for A313 stainless, 45 % for music wire, oil-tempered, chrome vanadium and chrome silicon, and 75 % in bending for torsion springs. It disagrees with Shigley on hard-drawn (45 against 40) and on stainless (35 against 40); both are carried.
Century Spring Corp., Extension Springs design guide. The published allowable stresses for extension springs: body wire “between 30 and 45 per cent of the material’s minimum tensile strength”, hook in torsion 30–45 % depending on material, hook in bending 75 %. More conservative than Shigley’s Table 10-7 for the body, and both are printed on the wire page.
R. C. Juvinall and K. M. Marshek, Fundamentals of Machine Component Design, chapter 17. Carried here because it DISAGREES with Shigley on the wire-strength constants — A_p = 2,170 MPa and m = 0.146 for music wire against 2,211 and 0.145, 1,750 and 0.192 for hard-drawn against 1,783 and 0.190 — and on the allowable, using a single S_sy = 0.4 S_ut where Shigley splits 0.45, 0.50 and 0.35 by material. Both readings are named on the wire page; neither is called a misprint.
ASTM A228/A228M, Standard Specification for Steel Wire, Music Spring Quality. Cited by number. The tensile strength of music wire is a function of diameter and the specification tabulates it; this page COMPUTES it from S_ut = A/d^m and checks the result against a named catalogue’s printed column rather than reproducing the standard’s table.
ASTM A227 (hard-drawn), A229 (oil-tempered), A232 (chromium-vanadium valve spring quality), A401 (chromium-silicon) and A313 (stainless steel spring wire); ASTM B159 for phosphor bronze. Cited by number. NOTE that at least one manufacturer’s published materials table labels A231 as chrome silicon: A231 and A232 are the chromium-VANADIUM specifications and A401 is the chromium-SILICON one. The designations on this page follow ASTM’s own scope titles.
Spring Manufacturers Institute, Handbook of Spring Design, and Associated Spring / Barnes Group, Design Handbook. The origin of the end-condition table, of the preferred initial-tension band plotted against spring index, and of the stability curves. Both are cited by name and NOT reproduced; the values used here were taken from the named catalogue and textbook printings below, which is this site’s standing policy on copyrighted design data.