4-40 UNC tap drill size and thread dimensions
4-40 UNC has a major diameter of 2.845 mm and a pitch of 40 threads per inch (0.6350 mm). Every other dimension below follows from those two numbers and the 60-degree thread form.
- Clearance hole
- 3.072
- Pitch diameter
- 2.4324
- Minor diameter of the nut thread
- 2.1574
- Minor diameter of the bolt thread
- 2.0657
- Tensile stress area
- 3.973 mm2
- Breaking load at that tensile strength
- 3178
- The old "diameter minus pitch" drill
- 2.210
- Engagement that rule actually gives
- 92.4 %
- Threads engaged over that length
- 6.77
- Equivalent threads per inch
- 40.000
Show the working
- Thread engagement = 75
- Clearance hole allowance = 8
- Length of engagement = 4.3
- Material tensile strength = 800
- major = 2.8447999999999993 = 2.8448
- p = 0.635 = 0.635
- h = 0.635 * 0.8660254037844386 = 0.549 926
- Tap drill = 2.8448 - 75/100 * 1.082532 * 0.635 = 2.329 24
- The old "diameter minus pitch" drill = 2.8448 - 0.635 = 2.2098
- Engagement that rule actually gives = 100 / 1.082532 = 92.376
- Pitch diameter = 2.8448 - 0.649519 * 0.635 = 2.432 36
- Minor diameter of the nut thread = 2.8448 - 1.082532 * 0.635 = 2.157 39
- Minor diameter of the bolt thread = 2.8448 - 1.226869 * 0.635 = 2.065 74
- Tensile stress area = pi/4 * (2.8448 - 0.938194 * 0.635)^2 = 3.972 71
- Clearance hole = 2.8448 * (1 + 8/100) = 3.072 38
- Breaking load at that tensile strength = 3.972 71 * 800 = 3178.17
- shear_area = pi * 2.157 39 * 4.3 * (0.5 + 0.57735 * (2.432 36 - 2.157 39)/0.635) = 21.8579
- Threads engaged over that length = 0.635 > 0 ? 4.3 / 0.635 : 0 = 6.771 65
- Equivalent threads per inch = 0.635 > 0 ? 25.4 / 0.635 : 0 = 40
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- tap drill = D - (engagement / 100) x 1.082532 x P
- pitch diameter = D - 0.649519 P
- internal minor diameter = D - 1.082532 P
- tensile stress area = (pi/4)(D - 0.938194 P)^2
The familiar "drill equals diameter minus pitch" rule actually produces about 92% thread engagement, not 75%. Past roughly 75% the extra holding power is negligible and the tapping torque rises sharply, which is why 75% or even 65% is the shop standard.
The tensile stress area formula is the ISO 898-1 definition, based on the mean of the pitch and minor diameters.
Cut a clearance hole rather than a close fit unless the joint is dowelled: thread clearance is what lets parts line up.
4-40 UNC at common engagements
| Engagement | Tap drill (mm) | Tap drill (in) |
|---|---|---|
| 65% | 2.398 | 0.0944 |
| 70% | 2.364 | 0.0931 |
| 75% | 2.329 | 0.0917 |
| 80% | 2.295 | 0.0903 |
| 85% | 2.261 | 0.0890 |
| 90% | 2.226 | 0.0876 |
Pick the nearest drill above the figure, never below it.
Frequently asked
What drill size do I need for 4-40 UNC?
2.33 mm (0.0917 in) for 75% thread engagement. The traditional rule gives 2.21 mm, which is a tighter and harder-tapping hole.
What is the pitch of 4-40 UNC?
40 threads per inch (0.6350 mm).
Where the numbers come from
- Thread geometry follows the ISO 68-1 basic profile shared by ISO metric and Unified inch threads; the stress-area definition is from ISO 898-1.