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Calculating the Size of the Tap Drill

I need to drill and tap a hole for 1x28 threads. To determine the size of the bore hole for the threads, I looked for the formula to calculate the size of the hole so the threads would be a 75% Full Thread. In the Machinery Handbook, I found this formula.

Hole size = Major Diameter - (1.08253 x % Full Thread) / (Threads per inch) Where % Full Thread is entered as 0.75

As a test, I used this formula to see how close I could match the table listed in the Handbook. As an example I picked 10-32 bolt, which according to the table requires a #21 drill (0.1590"). Using 75%, the above formula calculated a hole diameter of 0.1646". This is 0.056" larger than the hole specified in the table. This seems to be excessive.

In another machining book, I found the following formula for calculating hole diameter.

Hole size = Major Diameter - (1.299 x % Full Thread) / (Threads per inch) Where % Full Thread is entered as 0.75

Again as a test, I used this formula to see how close I could match the table listed in the Handbook. Again, I picked 10-32 bolt, which according to the table requires a #21 drill (0.1590"). Using 75%, the above formula calculated a hole diameter of 0.1595". This is 0.005" larger than the hole specified in the table. This seems to be more in line with the numbers in the table.

Why are there two different formulas? Which one is considered to be correct? Am I taking things out of context and this is why there is a difference? Are the tables based upon a different percentage? There was no percentage give for the table. Am I doing something wrong in the calculations? Appreciate any assistance. Thanks.

Bill

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