Original Question:

I am constructing a taper jig to use with my ShopSmith woodworking machine. Is there an already derived formula for conversion of taper (inches per foot) directly to degrees and vise versa. I used the tangent of the opposite side (taper) divided by one foot (12 inches, adjacent side of triangle) and then look up the degrees for the derived tangent for my right triangle. This is the answer but I thought perhaps you already have a quick and easy formula for this. Your help is appreciated. I really like your website. It has much useful information.

Click on this calculator link to open a calculator window.

Solution:

Figure 1 is an illustration of a typical taper jig used on a table saw. The other pictures show the mathematics of this taper jig and a suggestion to add a measuring device to set the jig taper directly in inches per foot.

Reader's response.

Thought you might like to see my completed Taper Jig. I used a 24 inch long board next to the work instead of a 12 inche one, so my separation of the "V" is in 1/2 inch increments instead of quarters of an inch.
i.e. 1/4 inch per foot on 12 inches is same as 1/2 per foot on 24 inch length.
I used tangent to calculate the angles in degrees for each setting. My scale goes from 1/4 inch per foot to 2 1/2 inches per foot and from 1.16 to 11.57 degrees. Note the taper in inches per foot is the left column and the degrees are in the right column.
Again, thank you so much for your help. I think I was on the right track, just need a little reassurance and coaching.