Finding pitch in degrees with a rise over run type formula

[astjp2]

Speaking of pitch, how would you figure out the pitch of a worm gear based on a screw pitch? For example, a 3/4x8 acme screw, what pitch is the worm gear for it? 14.5* pressure angle. Tim

 

[frbutts]

1 deg. equals .0174"per inch so run times 1 divided by .0174 equals degrees

 

[rangerman]

1 deg. equals .0174"per inch so run times 1 divided by .0174 equals degrees

That's an approximation adequate enough for very small angles of a few degrees, but it would create increasingly larger errors for angles greater than 10 degrees.
Or, to put it another way, .0174" rise for every 1" run is only mathematically exact for 1 degree angle.

Example: Tan 45° = 1 = [ .0174" rise over .0174" run ] , but it is not equal to .0174 x 45