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#3-56 UNF Tap Drill Size

The number you came for, then the reasoning behind it.

#3-56 UNF tap drill — 75% thread #45 0.0820" · 2.1 mm metric equivalent

How it's calculated

Tap drill = major diameter − (0.01299 × %thread) / TPI  →  0.0990 − (0.01299 × 75) / 56 = 0.0816"

The nearest standard drill above that is #45 at 0.0820".

All engagement percentages

% threadExact hole Inch drill Metric equivalent
50%0.0874"#44 (0.0860")2.2 mm
65%0.0839"#45 (0.0820")2.1 mm
75%0.0816"#45 (0.0820")2.1 mm
85%0.0793"#47 (0.0785")2 mm
Which percentage should you actually use?
75% for through-holes in mild steel and aluminium. 65% for blind holes, stainless, titanium and anything where the tap is at risk. 50% for hand-tapping deep holes. The strength you give up going from 75% to 60% is around 5%; the tapping torque you give up is around 30%. In practice the threads almost never fail — the tap does.

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