Worm and Hob: Lead Angle Calculator

The worm and hob lead angle calculator calculates the lead angle for a worm gear or gear hob based on its diametral pitch (1/in) or module (mm). This ultimately controls the spacing between teeth on the worm (just like the threads per inch, or pitch, of a screw). The pitch diameter of a worm gear or gear hob can be used as its effective diameter when calculating lead angle. Check out our diametral pitch calculator if you need to convert from circular pitch

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. The same is true for worms, where multiple starts will cause the wormgear to rotate faster. This can be accounted for by entering the number of starts.


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What is the Lead Angle?

Schematic of lead angle on a screw

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

How to Calculate Lead Angle

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.

Here's a Quick Summary:

Finer pitches have lower lead angles

Coarse pitches have higher lead angles

Units (inch or mm) need to be consistent