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.

Looking at a diagram of UN threads: enter image description herehttps://en.wikipedia.org/wiki/Screw_thread#/media/File:ISO_and_UTS_Thread_Dimensions.svg

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.


1 Answer 1


I don't know about those equations but thread percent should be the height of the trapezoid of the actual cut thread relative to the triangle of the theoretically ideal thread, regardless of how that ideal thread has been specified.

So 100% thread depth would be a thread that comes to a point (or a bit of the point removed if that was what has been specified to be a 100% thread). An actual thread has that point lopped off to form a trapezoid. In practice, I treat it as how much the tapped thread conforms to the tap profile.

If I drill a larger hole before tapping, then lower thread percentage because more of the peak forming the minor diameter is lopped off. If I drill a hole to match the minor diameter of the tap then 100% thread because none of the peak has been removed. 0% thread is where my tap drill is the same diameter as the major diameter of the tap. So much of the peak of the thread has been removed that there is no thread at all.

  • $\begingroup$ Afik this is the standard. 100% being a triangular profile where the diameter at the point is the major diameter of the fastener. $\endgroup$
    – Drew
    Mar 6, 2023 at 2:36

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