Thread Lead Angle Calculator

The thread lead angle calculator calculates the lead angle for a screw or bolt based on either the threads per inch, thread pitch, or lead. While English screws typically use the number of threads per inch, metric screws use pitch, which is the distance between two threads. Ultimately these are two ways of expressing equivalent information, we have a blog post outlining TPI and Pitch and one that covers the history of different screw threads.

Screws can also have multiple starts, which allow them to screw in faster, that is to cover more distance per revolution, while retaining original thread pitch. This can be accounted for by either entering the number of thread starts, or directly calculating the Lead. Lead is the linear travel the nut makes per one screw revolution. For a single start thread, lead is equal to the pitch. For multiple start screws, the lead is the pitch multiplied by the number of starts.

Find the right Spur Gear Calculator from our full list of free tools

The Lead Angle is the angle between the helix and its plane of rotation. In a screw, this is the angle the threads make relative to its rotation. One can imagine that as the thread pitch increases (finer threads, with closer spacing) each thread is closer to being vertical, and so the angle is less and less. Conversely, as threads get coarser each thread covers more length along the screw and so the angle increases

The Lead Angle is calculated based on the following formula:

where l is the lead, d is effective diameter, n is the number of thread starts, and P is the pitch.

Since the lead angle is unitless, the chosen units for dimensions don't matter as long as they are consistent. That is, if lead is given in mm, the diameter needs to be in mm as well. Likewise, both dimensions could be in inches, or anything else as long as they are the same.