Pick the wrong tap drill and you either snap the tap, strip the threads, or end up with a hole that fights you for the rest of the job. The math is simple — and it's the same math whether you're cutting on a Bridgeport, a CNC, or a hand drill in the field.

The two formulas

Imperial:   tap drill (in) = major Ø − (1 / TPI) × (% thread / 100)
Metric:     tap drill (mm) = major Ø − pitch × (% thread / 100)

major Ø   = nominal thread diameter
TPI       = threads per inch (UNC/UNF)
pitch     = mm per thread (M-series)
% thread  = 75 for general work, 60 for hard/tough alloys

That's it. Both formulas land on the same physics — you're just backing off from the major diameter by enough to leave the tap room to cut clean threads.

UNC tap drill chart (75% thread)

• #4-40 — drill #43 (0.0890")
• #6-32 — drill #36 (0.1065")
• #8-32 — drill #29 (0.1360")
• #10-24 — drill #25 (0.1495")
• 1/4-20 — drill #7 (0.2010")
• 5/16-18 — drill F (0.2570")
• 3/8-16 — drill 5/16" (0.3125")
• 1/2-13 — drill 27/64" (0.4219")
• 5/8-11 — drill 17/32" (0.5313")
• 3/4-10 — drill 21/32" (0.6563")

UNF tap drill chart (75% thread)

• #10-32 — drill #21 (0.1590")
• 1/4-28 — drill #3 (0.2130")
• 5/16-24 — drill I (0.2720")
• 3/8-24 — drill Q (0.3320")
• 1/2-20 — drill 29/64" (0.4531")
• 5/8-18 — drill 9/16" (0.5625")
• 3/4-16 — drill 11/16" (0.6875")

Metric tap drill chart (M-series, 75% thread, coarse)

• M3 × 0.5 — drill 2.5 mm
• M4 × 0.7 — drill 3.3 mm
• M5 × 0.8 — drill 4.2 mm
• M6 × 1.0 — drill 5.0 mm
• M8 × 1.25 — drill 6.8 mm
• M10 × 1.5 — drill 8.5 mm
• M12 × 1.75 — drill 10.2 mm
• M16 × 2.0 — drill 14.0 mm
• M20 × 2.5 — drill 17.5 mm

How to read a thread callout

• 1/4-20 UNC-2B — quarter-inch nominal Ø, 20 threads per inch, Unified National Coarse, class 2B (internal, medium fit)
• M8 × 1.25 — 6H — 8 mm nominal Ø, 1.25 mm pitch, 6H tolerance class (internal, medium fit)
• 1/4-20 UNC-3B — same as 2B but tighter fit, used for safety-critical fasteners

2B is the default for most shop work. 3B is for aerospace or anything where backlash kills you. UNC is coarse (faster to assemble, better for soft material). UNF is fine (more threads per inch, holds tighter, better for vibration).

When to drop to 60% thread

• Stainless 304 / 316 — work hardens, taps break easy
• Titanium and Inconel — same story, plus heat
• Hardened tool steel — anything over Rc 30
• Blind holes deeper than 2× diameter — chip evacuation problems
• Hand-tapping in awkward fixtures — less torque to break the tap

At 60% thread engagement you've still got about ~95% of the holding strength of a 75% thread (yes, really — the curve flattens fast above 60%) but you've cut tap breakage way down. Production shops have known this for decades.

Worked example: 1/4-20 in 304 stainless

Material:    304 stainless (work-hardens, tough on taps)
Thread:      1/4-20 UNC
Strategy:    drop to 60% thread engagement

tap drill = 0.250 − (1 / 20) × (60 / 100)
          = 0.250 − 0.05 × 0.6
          = 0.250 − 0.030
          = 0.220"

Closest standard drill: #2 (0.221") or letter A (0.234")
Pick #2 — it sits right at 60% engagement.
75% would have been #7 (0.201") — too tight for this material.

Common mistakes

• Using a 100% thread drill (the major diameter minus pitch) — the tap will fight you and probably snap.
• Forgetting peck depth on deep blind holes. Pull every 0.5–1× diameter to clear chips.
• Skipping the chamfer. A small countersink at the hole entrance keeps the tap straight.
• Tapping with no lubricant in stainless or aluminum. Tap Magic for steel, anhydrous IPA or kerosene for aluminum.

Run it on your phone

The ShopCalc app has a Tap Drill calculator that does this math for any thread (UNC/UNF/UNS/M-series) at any % engagement, plus the closest standard drill in either system. Plus speeds & feeds, drill chart, and metal weight. 100% offline, free on the App Store and Google Play.

Related

• How to calculate speeds and feeds for CNC machining
• ShopCalc: Machinist Calculator — free on iOS + Android
• Ace & Alan Tool — taps, end mills, drills

Note: Charts are starting points. Always verify against your tap manufacturer's recommended drill — a few makers (OSG, Emuge) publish their own charts that vary slightly for premium taps.