Taps one-quarter of an inch in diameter and smaller are, as a rule, made with V-threads whose sides form an included angle of 60 degrees, or, with round top and bottom threads. Taps larger than one-quarter inch are made with the United States Standard form of thread, which has an included angle of thread of 60 degrees, the same as the V-form, but with one-eighth of the altitude removed from the top and one-eighth filled in at the bottom, as shown in Fig. 118. The V-shaped thread taps are made in various pitches for each different size, but the United States Standard has a definite pitch for each diameter.

## Diameters

Below are given formulas for finding the diameters at the bottoms of threads, or tap-size drills for the V-thread, and the United States Standard thread. In both formulas, S = desired size; T=diameter of tap; N=number of threads per inch. Fig. 118. Form of U. S. Standard Thread.

S= T - 1.733 / N

### Formula For The United States Standard Thread

S=T - 1.3 / N

As an example of the working of the formulas, we will solve a problem by each.

(a) The tap size drill for a l 1/4-inch diameter by 6-thread V-tap may be derived by applying the formula for the V-thread, as follows:

S= 1 1/4 - 1.733 / 6

=1.25-.2888 = .961 in.

(b) The tap size drill for a 1-inch diameter by 8-thread U. S. S. tap may be derived by applying the formula for the United States Standard thread, as follows:

S = 1- 1.3 / 8

= 1-.1625 = .8375 in.