Thread and tap drill calculator
Pick a thread and an engagement percentage. You get the tap drill in both systems, plus the geometry behind it.
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How do you calculate tap drill size?
Subtract the thread depth you want from the nominal diameter: drill = D − (engagement ÷ 100) × 1.299 × pitch. The familiar shop rule of diameter minus pitch is that same formula at 77% engagement, which is why it has survived. An M8 × 1.25 at 75% engagement needs a 6.78 mm drill, so you reach for the standard 6.8 mm. Going to 100% engagement gains roughly 5% thread strength for about three times the tapping torque.
Why 75% is the shop standard
Thread strength does not rise in proportion to engagement. Going from 60% to 75% adds meaningful strength. Going from 75% to 100% adds around 5% — while roughly tripling the torque needed to cut it.
Since a tap fails in torsion, that trade is badly one-sided. In a blind hole in tough material the extra torque is exactly what snaps a tap off flush with the surface, turning a two-minute job into an afternoon with a carbide burr.
75% is not a compromise. It is close to the optimum for almost every practical case, which is why every tap drill chart is built around it.
The rule of thumb, and where it comes from
Every machinist knows the metric shortcut: tap drill equals diameter minus pitch. M8 × 1.25 gives 6.75 mm. M10 × 1.5 gives 8.5 mm.
It is not folklore. Substituting 77% engagement into the full formula gives almost exactly diameter minus pitch, because 0.77 × 1.299 ≈ 1.0, and the remaining difference falls inside normal drill tolerance. The shortcut is the formula, rounded to something you can do in your head.
That also tells you when not to trust it: at any engagement other than about 75%, work it out properly.
Coarse or fine, and when it matters
Coarse threads tap faster, tolerate damage and dirt better, and hold up in soft materials like aluminium and cast iron where a fine thread would strip. They are the default for good reason.
Fine threads have a larger minor diameter, so the bolt itself is stronger in tension, and they resist loosening slightly better under vibration. They also allow finer adjustment. The cost is fragility: a damaged fine thread is far less forgiving, and fine threads strip more readily in soft material.
For general fabrication, coarse. For thin-walled parts, adjustment mechanisms and high-tensile fasteners, fine.
The clearance hole nobody looks up
The tapped hole gets all the attention, but the part the bolt passes through needs a clearance hole, and drilling it at nominal diameter is a mistake. An M8 bolt through an 8 mm hole will bind on any misalignment at all.
ISO 273 defines three fits: close, medium and free. Medium is the sensible default for general work — 9 mm for an M8. The extra millimetre is what lets two parts actually come together.
The clearance figure above is the medium fit. Use close only where location genuinely matters, and free where thermal movement or tolerance stack-up is in play.
The formulas
Both ISO metric and Unified inch threads use the same 60° form, so one set of geometry covers both.
tap drill = D − (engagement% ÷ 100) × 1.299 × pitchpitch dia = D − 0.6495 × pitchminor dia = D − 1.0825 × pitchthread depth per side = 0.6134 × pitchD = nominal (major) diameterpitch = mm per thread (metric) = 25.4 ÷ TPI (inch)the shop rule: tap drill ≈ D − pitch (this formula at 77%)clearance hole, ISO 273 medium fit:M3 +0.4 M6 +0.6 M10 +1.0 M20 +2.0 M24 +3.0
Note the two different constants, because conflating them is the classic error. The minor diameter of the internal thread is D − 1.0825 × pitch. But percent-of-thread for tap drill selection is conventionally reckoned against a different reference height, giving 1.299. Every published tap drill chart uses 1.299, and using 1.0825 instead puts the drill about 3% of a diameter oversize at every size.
Inch threads are given as threads per inch rather than a pitch, so convert first: pitch in mm is 25.4 divided by TPI. A 1/4-20 UNC has a pitch of 1.27 mm, and the formula returns 0.2013 in — which is the #7 drill every chart lists for it.
Worked example: M8 × 1.25 at three engagements
A standard M8 coarse thread, tapped in aluminium, comparing engagement choices.
- At 100% — 8 − 1.00 × 1.299 × 1.256.38 mm
- At 75% — 8 − 0.75 × 1.299 × 1.256.78 mm
- At 60% — 8 − 0.60 × 1.299 × 1.257.03 mm
- Shop rule — 8 − 1.256.75 mm
- Clearance hole, medium fit9.00 mm
Reach for the standard 6.8 mm drill for 75% engagement, and a 9 mm for the clearance hole.
The 6.75 mm from the shop rule works out to 77% engagement — within a rounding error of the chart standard. That is exactly why the shortcut has survived a century of workshop use.
Common metric coarse threads and their 75% tap drills
- M3 × 0.5 — 2.51 mm, use 2.5 mm
- M4 × 0.7 — 3.32 mm, use 3.3 mm
- M5 × 0.8 — 4.22 mm, use 4.2 mm
- M6 × 1.0 — 5.03 mm, use 5.0 mm
- M8 × 1.25 — 6.78 mm, use 6.8 mm
- M10 × 1.5 — 8.54 mm, use 8.5 mm
- M12 × 1.75 — 10.30 mm, use 10.2 mm
Terms on this page
- Pitch
- The distance from one thread crest to the next. Metric threads state it directly in millimetres; inch threads state threads per inch instead, which is its reciprocal.
- Thread engagement
- How much of the theoretical full thread depth is actually cut. 75% is the shop standard because the strength beyond it is negligible and the tapping torque is not.
- Pitch diameter
- The imaginary diameter where thread and groove widths are equal. It is what a thread gauge actually measures and what determines fit.
- Clearance hole
- The hole in the part the bolt passes through, drilled larger than nominal so the parts can align. ISO 273 defines close, medium and free fits.
Common questions
What size drill for an M8 tap?
6.78 mm for the standard 75% engagement, so use the common 6.8 mm drill. The old shop rule of diameter minus pitch gives 6.75 mm, which works out to 77% engagement — near enough identical, which is why the shortcut has lasted.
How do you calculate tap drill size?
Drill = nominal diameter − (engagement ÷ 100) × 1.299 × pitch. At 77% engagement this reduces to diameter minus pitch, which is where the familiar shortcut comes from. Take care not to use the 1.0825 constant here — that one gives the minor diameter, not the tap drill.
Is 75% thread engagement enough?
Yes, for nearly every application. Going to 100% adds roughly 5% thread strength while roughly tripling tapping torque, and torque is what breaks taps. In practice the fastener fails before a 75% thread does.
What is the difference between coarse and fine threads?
Coarse threads tap faster, tolerate dirt and damage, and hold better in soft materials. Fine threads have a larger minor diameter so the bolt is stronger in tension, resist vibration slightly better, and allow finer adjustment — but strip more easily in soft material.
What size is a clearance hole for M8?
9 mm for a medium fit under ISO 273. Drilling it at 8 mm leaves no room for misalignment and the parts will bind. Use a close fit only where location genuinely matters.
Where these numbers come from
- ISO 261 — ISO general purpose metric screw threads, general plan The standard defining the metric coarse and fine pitch series used here.
- ISO 273 — Fasteners, clearance holes for bolts and screws The close, medium and free clearance hole series.
- ASME B1.1 — Unified inch screw threads The standard governing UNC and UNF inch threads.
Last verified 2026-08-01 The method on this page is checked against the sources above at least once a year. Spotted something out of date? Tell us and we will fix it.
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