2-56 UNC tap drill size and thread dimensions
2-56 UNC has a major diameter of 2.184 mm and a pitch of 56 threads per inch (0.4536 mm). Every other dimension below follows from those two numbers and the 60-degree thread form.
- Clearance hole
- 2.359
- Pitch diameter
- 1.8898
- Minor diameter of the nut thread
- 1.6934
- Minor diameter of the bolt thread
- 1.6279
- Tensile stress area
- 2.430 mm2
- Breaking load at that tensile strength
- 1944
- The old "diameter minus pitch" drill
- 1.731
- Engagement that rule actually gives
- 92.4 %
- Threads engaged over that length
- 7.28
- Equivalent threads per inch
- 56.000
Show the working
- Thread engagement = 75
- Clearance hole allowance = 8
- Length of engagement = 3.3
- Material tensile strength = 800
- major = 2.1843999999999997 = 2.1844
- p = 0.45357142857142857 = 0.453 571
- h = 0.453 571 * 0.8660254037844386 = 0.392 804
- Tap drill = 2.1844 - 75/100 * 1.082532 * 0.453 571 = 1.816 15
- The old "diameter minus pitch" drill = 2.1844 - 0.453 571 = 1.730 83
- Engagement that rule actually gives = 100 / 1.082532 = 92.376
- Pitch diameter = 2.1844 - 0.649519 * 0.453 571 = 1.8898
- Minor diameter of the nut thread = 2.1844 - 1.082532 * 0.453 571 = 1.693 39
- Minor diameter of the bolt thread = 2.1844 - 1.226869 * 0.453 571 = 1.627 93
- Tensile stress area = pi/4 * (2.1844 - 0.938194 * 0.453 571)^2 = 2.4297
- Clearance hole = 2.1844 * (1 + 8/100) = 2.359 15
- Breaking load at that tensile strength = 2.4297 * 800 = 1943.76
- shear_area = pi * 1.693 39 * 3.3 * (0.5 + 0.57735 * (1.8898 - 1.693 39)/0.453 571) = 13.1669
- Threads engaged over that length = 0.453 571 > 0 ? 3.3 / 0.453 571 : 0 = 7.275 59
- Equivalent threads per inch = 0.453 571 > 0 ? 25.4 / 0.453 571 : 0 = 56
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.
2-56 UNC at common engagements
| Engagement | Tap drill (mm) | Tap drill (in) |
|---|---|---|
| 65% | 1.865 | 0.0734 |
| 70% | 1.841 | 0.0725 |
| 75% | 1.816 | 0.0715 |
| 80% | 1.792 | 0.0705 |
| 85% | 1.767 | 0.0696 |
| 90% | 1.742 | 0.0686 |
Pick the nearest drill above the figure, never below it.
Frequently asked
What drill size do I need for 2-56 UNC?
1.82 mm (0.0715 in) for 75% thread engagement. The traditional rule gives 1.73 mm, which is a tighter and harder-tapping hole.
What is the pitch of 2-56 UNC?
56 threads per inch (0.4536 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.