# What is percent of thread depth when it comes to screws?

What, geometrically, is meant by percent thread depth? And, what would constitute 100% thread depth?

I have been trying to derive the equation for thread percentage in the textbook Machine Tool Practices (Kibbe et.al., ed. 10): $$Hole\ diameter = Outside\ diameter - \frac{0.1266 \times \%\ of\ thread\ depth}{threads\ per\ inch}$$ The book explains that tap drill charts usually show a 75% thread depth, because a greater percentage of thread does not increase the strength appreciably. It goes on to suggest using lower thread depths (50%-60%) for harder materials, to ensure the bolt breaks before the thread strips.

The problem arises when I try to find where the $$1.266$$ constant (lets call it $$\Gamma$$) comes from.

The pitch $$P$$ relates to $$H$$ by $$H = tan(60^\circ)\frac{P}{2}$$ And, then, the maximum thread depth would be where the whole flank is in contact. If "100%" thread depth means that the thread is engaged down the whole flank (from $$D_{maj}$$ to $$D_{min}$$), then (multiplied by two on the right to account for both sides) $$D_{maj}-D_{min} = 2\frac{5H}{8} = \frac{5}{8}tan(60^\circ)P$$ $$\Gamma = \frac{5}{8}tan(60^\circ) = 1.0825$$

This is different from the 1.266 given in the formula. Other sources give different numbers:

• A $$\Gamma = 1.299$$, basically that 100% thread uses a flank the height of $$\frac{7}{8}H$$
• B $$\Gamma = 1.0825%$$, same as mine
• C $$\Gamma = 1.2269$$, if you include the radius cut into the external thread to be $$H/12$$ in the 100% thread, even though the peaks of the internal thread will never reach it. This source doesn't really mention % depth, however
• D This thread has a lot of discussion. Several members suggest that the constant was carried over from a previous geometry. Whitworth would have $$\Gamma = \frac{2}{3}tan(62.5^\circ) = 1.2807$$ (I think) discounting that theory.

The problem seems to be in the fraction of H that constitutes 100% thread depth. Any guidance would be much appreciated.