Thread Engagement Length Calculator

How deep the tapped hole has to be so that the bolt breaks before the thread strips — derived from the shear areas rather than quoted as 1.5 diameters, with the strength of the tapped material as an input, both published criteria evaluated and the larger governing, and an explanation of where the rule of thumb comes from and where it fails.

Last updated 24 Sep 2026

Thread engagement length

Bolt and tapped material → engagement needed

Thread sizeThe engagement is set by the bolt’s tensile capacity against the tapped thread’s shear capacity, so both the stress area and the thread geometry come from this.

Bolt property class or gradeA stronger bolt needs a DEEPER hole, not a shallower one. The criterion is that the bolt breaks before the thread strips, so raising the bolt’s strength raises what the thread has to survive.

Material the hole is tapped inStrengths from MakeItFrom, one publisher throughout so the shear-to-tensile ratios are comparable. Grey cast iron is the odd one out and the page says why.

Tensile strength of that material (N/mm²)Used by the published strength-ratio method.

Shear strength of that material (N/mm²)Used by the shear-area method. If you only have a tensile figure, 0.6 of it is the usual convention — but note that it is badly wrong for cast iron, where shear exceeds tensile.

Engagement you actually have (mm)The depth of full-form thread the bolt engages, not the drilled depth. Allow for the incomplete threads at the top of a tapped hole and for the lead on a bottoming tap.

Not a circuit: the same bolt threaded into two bosses, both drawn to the same scale, with the required engagement dimensioned on each. The left-hand boss is a member as strong as the bolt — which is the case a standard nut covers, and it needs about 0.8 diameters. The right-hand boss is the material you chose, and the difference between the two depths is the whole content of this page: a 6061-T6 aluminium boss needs about two and a half times what a steel one does, for the same bolt, because the criterion scales with the ratio of the two tensile strengths. The double line across the right-hand boss is the engagement you said you HAVE. If it sits above the bottom of the dimensioned depth, the tapped thread is the weak link — and a stripped thread gives no warning and leaves no residual strength, where a bolt necks visibly first. The bolt's diameter is drawn at 26 units whatever size you pick, so the figure is a ratio drawing: what is to scale is the depth against the diameter.

21.11mmExample

M10 class 8.8 into a 6061-T6 aluminium boss, with 15 mm of thread engaged

Two published criteria, and the larger of them

Method A: Lₑ = 2A_s / (0.5π d₂) · max(1, R_m,bolt / R_m,internal) · Method B: Lₑ = A_s R_m,bolt / (A_n’ · τ_internal) · A_n’ = 0.875 π d · A_s’ = 0.75 π d₁ · required = max(A, B)

Lₑ: length of thread engagement — full form thread only, not the drilled depth
A_s: tensile stress area of the bolt, from the stress-area page. The thing that has to break first
d₂: pitch diameter. Method A’s denominator is half the pitch cylinder, which is a convention: the real geometric shear surface is 1.5 to 1.75 times bigger
A_n’: internal (tapped) thread shear area per millimetre of engagement. The circumference at the bolt’s major diameter times the 0.875 P axial thickness of nut thread there
A_s’: external (bolt) thread shear area per millimetre. At the internal thread’s minor diameter the bolt thread is 0.75 P thick, so this is always the smaller of the two — by 1.2 to 1.4 times
R_m: minimum tensile strength. Method A works entirely from tensile strengths, which is what makes it wrong for cast iron
τ: shear strength of the tapped material. A published property for metals, roughly 0.6 of tensile — except in grey cast iron, where it is 1.3 times tensile

Worked example

M10 class 8.8 into a 6061-T6 aluminium boss, with 15 mm of thread engaged
The bolt breaks at A_s R_m = 57.99 × 800 = 46.39 kN. Everything else has to beat that
Baseline: a member as strong as the bolt needs 2 A_s / (0.5π d₂) = 2 × 57.99 / (0.5π × 9.026) = 8.18 mm, which is 0.818 diameters. An ISO 4032 nut for an M10 is 8.04 mm high at minimum — the criterion and the nut standard land on the same answer, which is the check that it is calibrated
6061-T6 is 310 N/mm² tensile, so the strength ratio is 800/310 = 2.581. Method A: 2.581 × 8.18 = 21.11 mm, or 2.11 diameters
Method B works from the geometry instead. The tapped thread's shear area is 0.875π × 10 = 27.49 mm² per millimetre of engagement, and 6061-T6 shears at 210 N/mm², so it strips at 5,773 N per millimetre. To beat 46.39 kN needs 8.04 mm
The two disagree by 2.63 times, and the page takes the larger: 21.11 mm, 2.11 diameters. With 15 mm engaged you are 6.11 mm short, and the honest answer is a deeper hole, a thread insert, or a larger bolt
For contrast: the same bolt into a steel nut of its own strength needs 8.18 mm and into a grey iron boss method A says 26.2 mm while method B says 5.1 mm — a factor of 5.1, because cast iron's shear strength is above its tensile strength and method A cannot see that
And the 1.5 d rule of thumb? 15 mm on an M10. It is exactly right at a strength ratio of 1.83 — an 800 N/mm² bolt into a member of about 436 N/mm², which is ordinary structural steel. In aluminium it is 30% short, in magnesium and filled nylon it is less than half of what is needed, and for a steel nut it is nearly twice what is needed

An M10 class 8.8 bolt into each material, by both criteria

Read the aluminium row first: 2.1 diameters against 0.8 for a steel nut of the bolt’s own strength, which is the “aluminium needs about twice the engagement” rule arriving from the strengths rather than from folklore. True Precision Machining’s published guidance for the same method — about 1× diameter steel into steel, about 2× into 6061-T6, over 2.5× into magnesium and plastics — is reproduced here with nothing fitted to it. Now read the grey cast iron row, which is why this page prints two columns. Cast iron’s SHEAR strength is 330 N/mm² against a tensile strength of 250: a ratio of 1.32 where every other material on the list is near 0.6. Method A works from tensile strength and therefore asks for 2.6 diameters; method B works from shear strength and asks for 0.5. They differ by a factor of five, and the page takes the larger because being wrong here is a safety matter. Rows marked * have a shear strength this batch could not source and took at 0.6 of tensile — for those the two methods are not independent. 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.
Tapped material	R_m (N/mm²)	Shear (N/mm²)	Shear ÷ R_m	Method A (mm)	Method A (× d)	Method B (mm)	Method B (× d)	Governing (× d)
Structural steel, ASTM A36 / S275	480	300	0.63	13.6	1.36	5.6	0.56	1.36
Grey cast iron, ASTM class 35 / EN-GJL-250	250	330	1.32	26.2	2.62	5.1	0.51	2.62
Aluminium 6061-T6	310	210	0.68	21.1	2.11	8.0	0.80	2.11
Magnesium AZ91D (die cast)	190	130	0.68	34.4	3.44	13.0	1.30	3.44
Free-cutting brass C36000	430	260	0.60	15.2	1.52	6.5	0.65	1.52
PA66 with 30% glass fibre, dry*	190	114	0.60	34.4	3.44	14.8	1.48	3.44
Steel of a class 8 nut, for reference*	800	480	0.60	8.2	0.82	3.5	0.35	0.82

The baseline engagement, size by size, and the two thread shear areas

The baseline column is the engagement a member as strong as the bolt needs, and it lands between 0.78 and 0.86 of the diameter at every size. That is not a coincidence, and it is the independent check that the criterion is calibrated: ISO 898-2 designs a nut so that the bolt breaks before the nut strips, and an ISO 4032 nut’s minimum height is 0.80 to 0.88 of the diameter. The criterion and the nut standard agree to within 25% at every size from M5 to M36 without either being fitted to the other. The last three columns are computed from the basic thread profile: the axial thickness of bolt thread at the nut’s minor diameter is 0.75 P and of nut thread at the bolt’s major diameter is 0.875 P, which this batch verified by sampling the ISO 68-1 profile at two hundred thousand points per pitch. The nut thread always has more area than the bolt thread, by 1.2 to 1.4 times — which is exactly why a standard steel nut does not strip. 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	Pitch (mm)	A_s (mm²)	Baseline Lₑ (mm)	Lₑ ÷ d	Threads engaged	Internal shear area (mm²/mm)	External shear area (mm²/mm)	Internal ÷ external
M4	0.70	8.8	3.15	0.788	4.5	11.00	7.64	1.439
M5	0.80	14.2	4.03	0.806	5.0	13.74	9.74	1.411
M6	1.00	20.1	4.79	0.798	4.8	16.49	11.59	1.423
M8	1.25	36.6	6.48	0.811	5.2	21.99	15.66	1.404
M10	1.50	58.0	8.18	0.818	5.5	27.49	19.74	1.393
M12	1.75	84.3	9.88	0.823	5.6	32.99	23.81	1.385
M14	2.00	115.4	11.57	0.827	5.8	38.48	27.89	1.380
M16	2.00	156.7	13.57	0.848	6.8	43.98	32.60	1.349
M18	2.50	192.5	14.96	0.831	6.0	49.48	36.03	1.373
M20	2.50	244.8	16.96	0.848	6.8	54.98	40.75	1.349
M22	2.50	303.4	18.96	0.862	7.6	60.48	45.46	1.330
M24	3.00	352.5	20.35	0.848	6.8	65.97	48.90	1.349
M27	3.00	459.4	23.35	0.865	7.8	74.22	55.97	1.326
M30	3.50	560.6	25.74	0.858	7.4	82.47	61.76	1.335
M36	4.00	816.7	31.13	0.865	7.8	98.96	74.62	1.326

The engaged threads do not share the load, and the first one takes most of it

Measured on a preloaded M10 × 1 with a standard uniform-pitch nut by Croccolo and colleagues in *Mechanics & Industry*, following Sopwith’s 1948 analytical model: about 38% on the first engaged thread, 24% on the second, 15% on the third and 11% on the fourth — 88% of the load in four threads. Two consequences that matter. First, both criteria on this page assume the shear stress is uniform along the engagement, and it is not; that is part of why the criteria carry factors rather than being a pure strength comparison. Second, engagement beyond about five threads adds very little capacity — so a very deep hole in a strong material is wasted machining, while a shallow hole in a weak one cannot be rescued by going deeper indefinitely, because the load never reaches the bottom threads. In a soft material the thread yields locally and the load DOES redistribute, which is one of the few ways aluminium behaves better than steel here. 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.
Thread, counting from the loaded face	Share of the axial load (%)	Cumulative (%)	Load on it at bolt fracture, M10 class 8.8 (kN)
1	38	38	17.63
2	24	62	11.13
3	15	77	6.96
4	11	88	5.10
5 and beyond	12	100	5.57

Why this failure mode is the dangerous one

This is why the criterion is asymmetric, and why every published method carries a factor rather than simply comparing two strengths. You WANT the bolt to be the weak link. A bolt that yields gives warning, keeps carrying load and can be replaced with an identical part; a stripped boss in a casting can write off the casting. The practical rule that follows: when the two criteria on this page disagree, take the deeper hole. Machining is cheaper than a thread insert and very much cheaper than a casting. 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.
Failure	Warning you get	What is left afterwards
Bolt yields in tension	Visible. The bolt necks, the thread pitch stretches locally, and a bolt that has yielded is measurably longer than a new one	The bolt is still carrying load, and still carrying most of it. A yielded bolt has passed its proof load, not its tensile strength
Bolt breaks in tension	None at the moment of failure, but the bolt can be inspected and a torque check finds it	Nothing, but the failure is local to one fastener and the fracture face tells you what happened
Tapped thread strips	NONE. The thread shears progressively, thread by thread, and it often happens during tightening while the wrench still reads a plausible torque — because the torque is mostly friction and a stripping thread still generates friction	NOTHING. A stripped thread has no residual strength and cannot be retightened. The hole is bigger than the bolt and the repair is a thread insert, a larger bolt, or a new part

The criterion, where 1.5 d comes from, and the material that breaks one of the two methods

The question this page answers is how deep the tapped hole has to be so that the bolt breaks before the thread strips. That is the right way round on purpose. A bolt that yields necks visibly, keeps carrying load and can be swapped for an identical part. A stripped thread gives no warning at all — it often happens during tightening, while the wrench is still reading a plausible torque, because the torque is mostly friction and a shearing thread still generates friction — and it leaves nothing behind. The hole is bigger than the bolt and the repair is an insert, a larger fastener, or a new casting.

The criterion is a strength ratio, not a rule of thumb, and the rule of thumb falls out of it. The published simplified method, stated identically by Engineers Edge and by True Precision Machining and traceable to FED-STD-H28/2B, requires the thread shear area to be at least twice the bolt’s tensile stress area, which gives Lₑ = 2A_s/(0.5π d₂), and then multiplies by the ratio of tensile strengths when the tapped material is weaker. Evaluate the baseline across the metric series and it lands between 0.78 and 0.86 of the diameter at every size — which is the height of a standard nut. That is the independent check that the criterion is calibrated correctly: ISO 898-2 designs a nut so the bolt fails first, and an ISO 4032 nut’s minimum height is 0.80 to 0.88 d. Two methods, two standards, one answer, nothing fitted.

So where does “1.5 × diameter” come from? A strength ratio of 1.83. Work backwards: 1.5 d divided by the 0.818 d baseline is 1.83, which is an 800 N/mm² bolt into a member of about 437 N/mm² — ordinary structural steel. The rule is right for the commonest case in the world and has no way of knowing about anything else. In 6061-T6 the same bolt needs 2.1 diameters; in AZ91D magnesium or 30% glass-filled nylon it needs 3.4; for a nut of its own strength it needs 0.8, so 1.5 d is nearly double what a through-bolted joint requires. The rule fails in both directions and it fails silently.

The second method exists because the first one cannot see cast iron. Compute the tapped thread’s geometric shear area from the basic profile — the circumference at the bolt’s major diameter times the 0.875 P axial thickness of nut thread there, a construction this batch verified by sampling the ISO 68-1 profile rather than trusting the algebra — and compare its capacity at the material’s published SHEAR strength against the bolt’s tensile capacity. For most metals the two methods land within a factor of two of each other, with method A the conservative one. For grey cast iron they differ by a factor of five, because cast iron’s shear strength is 330 N/mm² against a tensile strength of 250 — a ratio of 1.32 where every other material on the list is near 0.6. Graphite flakes behave like cracks in tension and hardly matter in shear. Method A, working from tensile strength, is badly pessimistic there; this page prints both and takes the larger, and says which one governed.

And the threads do not share the load. Measured on a preloaded M10 by Croccolo and colleagues, following Sopwith’s 1948 model: 38% of the axial load on the first engaged thread, 24% on the second, 15% on the third, 11% on the fourth — 88% in four threads. Both criteria here assume uniform shear along the engagement, which is part of why both carry factors. It also means engagement beyond about five threads buys very little, so a very deep hole in a strong material is wasted machining and a shallow hole in a weak one cannot be rescued by going deeper without limit. The bolt’s own capacity comes from the proof load and tensile stress area calculator, the torque that loads it from the bolt torque calculator, and how much of that preload you can actually count on from the preload accuracy by tightening method calculator.

Frequently asked questions

How deep should a tapped hole be for a bolt?

It depends on the material, and the range is wider than the rule of thumb suggests. For a steel bolt into steel of comparable strength, about 1 diameter — which is why a standard nut is 0.8 to 0.88 d high. For a class 8.8 bolt into ordinary structural steel, about 1.4 d, which is where the familiar 1.5 d comes from. Into 6061-T6 aluminium, about 2.1 d. Into magnesium or a glass-filled polymer, 3.4 d and a warning about creep. The page computes it from the two strengths rather than quoting a table, and prints both published criteria because they disagree.

Why does aluminium need about twice the engagement steel does?

Because the criterion scales with the ratio of the bolt’s tensile strength to the tapped material’s. A class 8.8 bolt is 800 N/mm²; 6061-T6 is 310. The ratio is 2.58, and applied to the 0.82 d baseline it gives 2.1 diameters. That is the “twice as deep in aluminium” rule arriving from arithmetic. Note that it is the ratio that matters, not the aluminium: a class 4.6 bolt into 6061-T6 has a ratio of 1.29 and needs only about 1.1 diameters, and the honest way to solve a shallow boss is often a weaker bolt rather than a deeper hole.

Where does the 1.5 × diameter rule come from, and when is it wrong?

It corresponds to a strength ratio of 1.83 — a high-tensile bolt into ordinary steel. It is wrong and unsafe in aluminium (needs 2.1 d), in magnesium and filled polymers (3.4 d), and for a 12.9 bolt into anything soft. It is wrong and wasteful for a nut or a hole in material as strong as the bolt, which needs only 0.8 d. And it is ambiguous in cast iron, where the two published criteria differ by a factor of five. The page plots the rule as a line against both criteria so you can see where it crosses.

Should I use the tensile strength or the shear strength of the tapped material?

The two published methods use different ones, which is the problem. The strength-ratio method scales by tensile strengths, which implicitly assumes every material’s shear strength is the same fraction of its tensile strength — about 0.6, which is true for the steels, the aluminium alloys, the magnesium and the brass on this page. It is not true for grey cast iron, whose shear strength is 1.32 times its tensile strength. The shear-area method uses the shear strength directly and is the physically relevant one, but it also assumes the shear stress is uniform along the engagement, which it is not. This page computes both and reports the larger.

Does a coarse or a fine thread give better engagement?

A coarse thread gives more shear area per millimetre of engagement, because the shear area per millimetre is 0.875πd for the internal thread regardless of pitch, while the bolt’s stress area is larger for a fine thread. So on the criterion here, the fine thread needs slightly MORE engagement — it has more tensile capacity to protect. In soft materials coarse threads are preferred for a different and stronger reason: a coarse thread has a thicker root in the soft material and is much harder to damage during assembly. Note that the pitch and thread-series tables themselves belong to the converters plugin, not here.

What about a threaded insert?

It is the right answer whenever the computed engagement will not fit, and it is what production designs do rather than machining a very deep hole in a soft casting. An insert replaces the problem with two: a steel internal thread for the bolt, which is the easy case at about 0.8 d, and a much larger-diameter external thread engaging the soft material over the insert’s own length — larger diameter means more shear area per millimetre, so it works. This page does not size inserts, because the geometry is the maker’s and every maker’s is different; use their published pull-out data.

Related calculators

References

FED-STD-H28/2B, Screw-Thread Standards for Federal Services, Section 2: Unified Inch Screw Threads, and the same method in Machinery’s Handbook. Cited by section. The thread shear areas on this page are computed from the basic profile rather than copied: the axial thickness of the bolt thread at the internal thread’s minor diameter is P/2 + tan 30° (d₂ − d₁) = 0.75 P, and of the nut thread at the bolt’s major diameter is P/2 + tan 30° (d − d₂) = 0.875 P, which is the same construction the standard’s 0.57735 terms describe.
True Precision Machining. Thread Engagement Length Calculator, and Engineers Edge’s Minimum Thread Engagement Equation. Two independent statements of the same published simplified method: the shear area must be at least twice the tensile stress area, giving Lₑ = 2Aₜ / (0.5π(D − 0.64952 p)), and a strength ratio J = UTS_bolt/UTS_internal applied when it exceeds 1. TPM’s guidance figures — about 1× diameter steel into steel, about 2× into 6061-T6, more than 2.5× into plastics and magnesium — are what the method reproduces here from the strengths alone.
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.
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.
MakeItFrom.com material property pages for ASTM A36 / S275 structural steel, ASTM class 35 / EN-GJL-250 grey cast iron, 6061-T6 aluminium, AZ91D magnesium, C36000 free-cutting brass and dry 30% glass-fibre PA 6/6. One publisher throughout, so the shear-to-tensile ratios on this page are comparable with each other. The grey iron row is the one worth looking at: 250 N/mm² tensile against 330 N/mm² shear, a ratio of 1.32, where every other material on the list is near 0.6.
Penticton Foundry. Gray Iron ASTM A48 Class 30 Data Sheet. Cited for the compressive strength of grey iron, “109 (752)” ksi and N/mm² against a tensile strength of “30,000 psi (207 MPa)” — a factor of 3.6, which is the same anisotropy that puts its shear strength above its tensile strength.
D. Croccolo, M. De Agostinis, S. Fini, G. Olmi et al., Achieving uniform thread load distribution in bolted joints using different pitch values, Mechanics & Industry 21 (2020) 607. Source for the load share of the engaged threads of a preloaded M10 × 1 bolt with a standard uniform-pitch nut: about 38% on the first thread, 24% on the second, 15% on the third and 11% on the fourth. It states that “in a preloaded bolt the first threads in contact withstand most of the axial load, and consequently the failure generally takes place in the first thread turn in contact between the bolt and nut”, and cites D. G. Sopwith, The Distribution of Load in Screw Threads, Proc. I.Mech.E. 159 (1948) 373, as the classical analytical model.
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.