Calculating angles on an X leg table

 Blog entry by Woodknack posted 11-18-2017 06:06 AM 1796 reads 1 time favorited 5 comments

I’m putting this here so the next time someone asks this question, I can find the information quickly. I have not tried these. Feel free to comment.

Calculating the angles of an X leg table is deceptively complicated because the width of the legs or braces changes the angles. Here are some alternatives to calculating the angle:
• Tack the legs or braces together in an X and arrange them to the right angle.
• Make a mock up from cardboard or plywood
• Draw it full size on paper or plywood
• Use a drawing program like Sketchup, etc.

But if you want to try and calculate the answer, maybe this will help…

Let B be the angle (initially unknown) the leg makes with the floor.
Let T be the thickness of the leg stock.
Let W be the width of outer sides of the X.
Let H be the height of the top of the X from the floor (i.e. the height of the under side of the table top.)
And let F be the width of the foot of the X legs (i.e. the length of the diagonal cut across the leg stock.)

Then sin(B) = T/F (looking at the triangle made by the foot and the thickness)
and
sin(B) = H / sqrt((W – F)^2 + H^2) (looking at the triangle the whole leg makes with the floor.)

Setting the two right sides equal and solving for F, (yeah, it s a mess) will let you compute the angle B (arcsin(T/F)). Then the angle you want is 180 – 2B. (Remember to convert arcsin(T/F) to degrees first.)

Just for reference (and to check my typing skills)

F =( (2T^2W) +/- sqrt((4T^4W^2)-4(T^2-H^2)) )/ 2(T^2-H^2)

(I told you it was a mess.)

- GeBeWubya

JBay found this calculator, but I haven’t tried it.

The math is over my head, Sketchup, it only takes a few minutes.
I did find this, (if it works) There is a calculator on the right side you can try.
http://jsfiddle.net/h1xda7qm/

- jbay

-- Rick M, http://thewoodknack.blogspot.com/