7/8-9 UNC tap drill size and thread dimensions
7/8-9 UNC has a major diameter of 22.225 mm and a pitch of 9 threads per inch (2.8222 mm). Every other dimension below follows from those two numbers and the 60-degree thread form.
- Clearance hole
- 24.003
- Pitch diameter
- 20.3919
- Minor diameter of the nut thread
- 19.1699
- Minor diameter of the bolt thread
- 18.7625
- Tensile stress area
- 301.017 mm2
- Breaking load at that tensile strength
- 240 814
- The old "diameter minus pitch" drill
- 19.403
- Engagement that rule actually gives
- 92.4 %
- Threads engaged over that length
- 11.80
- Equivalent threads per inch
- 9.000
Show the working
- Thread engagement = 75
- Clearance hole allowance = 8
- Length of engagement = 33.3
- Material tensile strength = 800
- major = 22.224999999999998 = 22.225
- p = 2.822222222222222 = 2.822 22
- h = 2.822 22 * 0.8660254037844386 = 2.444 12
- Tap drill = 22.225 - 75/100 * 1.082532 * 2.822 22 = 19.9336
- The old "diameter minus pitch" drill = 22.225 - 2.822 22 = 19.4028
- Engagement that rule actually gives = 100 / 1.082532 = 92.376
- Pitch diameter = 22.225 - 0.649519 * 2.822 22 = 20.3919
- Minor diameter of the nut thread = 22.225 - 1.082532 * 2.822 22 = 19.1699
- Minor diameter of the bolt thread = 22.225 - 1.226869 * 2.822 22 = 18.7625
- Tensile stress area = pi/4 * (22.225 - 0.938194 * 2.822 22)^2 = 301.017
- Clearance hole = 22.225 * (1 + 8/100) = 24.003
- Breaking load at that tensile strength = 301.017 * 800 = 240 814
- shear_area = pi * 19.1699 * 33.3 * (0.5 + 0.57735 * (20.3919 - 19.1699)/2.822 22) = 1504.09
- Threads engaged over that length = 2.822 22 > 0 ? 33.3 / 2.822 22 : 0 = 11.7992
- Equivalent threads per inch = 2.822 22 > 0 ? 25.4 / 2.822 22 : 0 = 9
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.
7/8-9 UNC at common engagements
| Engagement | Tap drill (mm) | Tap drill (in) |
|---|---|---|
| 65% | 20.239 | 0.7968 |
| 70% | 20.086 | 0.7908 |
| 75% | 19.934 | 0.7848 |
| 80% | 19.781 | 0.7788 |
| 85% | 19.628 | 0.7728 |
| 90% | 19.475 | 0.7667 |
Pick the nearest drill above the figure, never below it.
Frequently asked
What drill size do I need for 7/8-9 UNC?
19.93 mm (0.7848 in) for 75% thread engagement. The traditional rule gives 19.40 mm, which is a tighter and harder-tapping hole.
What is the pitch of 7/8-9 UNC?
9 threads per inch (2.8222 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.