Short answer: for 1/2-13 UNC at 75% thread engagement, the calculated tap drill is 0.4251". The closest commercial drill that hits ~75% is 27/64" (0.4219"), which actually produces about 78% engagement — slightly tighter than 75% but the standard machinist call. If your tap is dying or the material is gummy (304 stainless, 6Al-4V titanium), drop to 60% engagement and use 7/16" (0.4375"). Both are below.

The formula

Tap drill = D − (% engagement / 100) × 1.299 × P

D     = nominal major diameter (inches)
P     = thread pitch (inches per thread = 1 / TPI)
1.299 = 2 × √3/3 (geometry of a 60° UN thread)

Quick way to verify: 100% engagement would mean the drill equals the thread minor diameter. The formula above with 100% gives that exact value (within rounding). Anything less than 100% leaves a little flat at the root of the cut thread — which is what you want, because cutting the last 25% of the thread takes 50% of the torque and gives you almost no extra strength.

Worked example: 1/2-13 UNC at 75%

D    = 0.500"
TPI  = 13
P    = 1 / 13 = 0.07692"

Tap drill = 0.500 − 0.75 × 1.299 × 0.07692
          = 0.500 − 0.07497
          = 0.42503"

Closest fractional drill below: 27/64" = 0.42188"
Closest letter drill below:     none higher than 27/64" applicable
Closest decimal drill (over 1/64): 0.4219" or 0.4250"

The 27/64" drill (0.4219") is what every tap chart prints for 1/2-13 UNC. It actually produces 78% engagement, not 75%, because commercial drills don't come in 0.4250". If you want exactly 75% you'd need a 0.4250" drill (which exists, but it's a custom/oversize and you won't find it in a standard index).

Worked example: 1/2-13 UNC at 60% (gummy materials)

D    = 0.500"
TPI  = 13
P    = 0.07692"

Tap drill = 0.500 − 0.60 × 1.299 × 0.07692
          = 0.500 − 0.05997
          = 0.44003"

Closest fractional drill: 7/16" = 0.4375"
This actually gives ~63% engagement — close enough.

When to drop from 75% to 60%

• 304 / 316 stainless — work-hardens. 75% taps die fast; 60% engagement keeps the load down.
• Titanium 6Al-4V — same problem, worse. 60% always.
• Hand tapping (no machine) — 60% lets you turn the wrench without snapping the tap.
• Aluminum & brass — can stay at 75% — the materials are soft enough.
• Mild steel (1018, A36) — 75% is fine, 65% is faster.
• Tool steel D2 / O1 annealed — 65–70% sweet spot.
• Cast iron — 75%, soft on taps.

The strength-of-thread tradeoff: dropping from 75% to 60% reduces the thread's static pull-out strength by less than 5%, but the torque required to cut the thread drops by about 30%. Almost always a good trade.

The complete chart for 1/2-13 UNC

Engagement   Calculated TD   Standard drill   Actual %
50%          0.4500"         29/64" (0.4531") ~46%
55%          0.4451"         29/64" (0.4531")  53%
60%          0.4400"         7/16" (0.4375")   63%
65%          0.4350"         7/16" (0.4375")   67%
70%          0.4301"         27/64" (0.4219") 84%   ← gap
75%          0.4251"         27/64" (0.4219") 78%
80%          0.4201"         27/64" (0.4219") 78%
85%          0.4150"         13/32" (0.4063")100%+ ← over-cut
90%          0.4100"         13/32" (0.4063")100%+

Notice the gap between 65% and 75%: there's no commercial drill between 7/16" (0.4375) and 27/64" (0.4219). If you want exactly 70%, you'd need a 0.4301" drill, which means buying a metric (10.9mm = 0.4291") or an oversize letter drill. In practice: stop at 65% with 7/16" or jump to 78% with 27/64".

Other UNC tap drills people search for

• 1/4-20 UNC, 75% — #7 (0.201") is the chart number; calculated 0.2026".
• 5/16-18 UNC, 75% — F (0.257"); calculated 0.2569".
• 3/8-16 UNC, 75% — 5/16" (0.3125"); calculated 0.3147".
• 7/16-14 UNC, 75% — U (0.368"); calculated 0.3681".
• 1/2-13 UNC, 75% — 27/64" (0.4219"); calculated 0.4251".
• 5/8-11 UNC, 75% — 17/32" (0.5313"); calculated 0.5364".
• 3/4-10 UNC, 75% — 21/32" (0.6563"); calculated 0.6526".
• 1-8 UNC, 75% — 7/8" (0.8750"); calculated 0.8783".

Tap-drill rules of thumb people repeat that are wrong

• "Just use the major diameter minus the pitch." That's 100% engagement. You'll snap the tap.
• "Use the next size up for stainless." Vague. The right move is to drop the engagement %, then pick the drill that matches the new TD.
• "Same drill for UNC and UNF at the same diameter." No. UNC has a coarser pitch — UNF needs a smaller (closer-to-major) drill.
• "Drill = thread root." The root has the flat, the drill is slightly larger so the tap doesn't bottom on the root form.

Cutting tap vs forming tap

The formula above is for cutting taps (M1, M3, spiral-flute, etc.) which remove material to form the thread. Forming (roll) taps displace material rather than cut, and they need a larger drill: about 0.005" + major diameter × 0.5" for inch threads, or follow the manufacturer's drill chart. Roll taps in 1/2-13 typically call for 0.470–0.475" drill (12.0–12.1mm).

Run it on your phone

The ShopCalc app has the full UNC, UNF, and ISO metric tap drill chart at 50, 60, 65, 70, 75, 80, and 85% engagement — plus the formula behind it and roll-tap drill sizes. 100% offline. Free on the App Store and Google Play.

Related

• Tap drill chart and how to read thread sizes (UNC, UNF, M-series)
• Speeds and feeds for 1/4" 4-flute carbide in 4140
• ShopCalc — machinist calculator on iOS + Android

Note: Always verify on scrap before tapping a real part. A snapped tap costs more than a wasted scrap block, every time.