How To Calculate Length Of Screw Thread? I'm having a tough time searching for the answer to this as most of the results are in the realm of mechanical engineering and appear to be unrelated, I apologize if this is a really obvious question.
Say there is a circular arc in $2$ dimensions covering $90$ degrees at a radius of $21$. I know the length of the arc would be $\frac{21}{2}\pi$ or about $32.99$, but what if it were then stretched through the third dimension by some number $x$?  How do you calculate the screw thread length?

As an intuitively convincing method, you could consider straightening out the arc into a line of length $\frac{21}2\pi$ and then stretching it along another axis by length x and using Pythagorean theorem to calculate its new length: $\sqrt{(\frac{21}2\pi)^2+x^2}$.
