I recently ran across an article from the Fine Homebuilding website regarding methods for laying out a true ellipse. As many of the commenters noted, the method shown did not produce a true classic ellipse, but an arc segment.

  In riding around looking at the arches constructed on many new homes, more often than not a rather poor job was done in creating nicely proportioned arches, and true ellipses seem to be about nonexistent.

  Here is a method shown to me which I have found to be a practical method to produce some really nice looking elliptical archways.

  The first step is to determine the overall width of the “rough” opening, allowing for brick, drywall or casing. Then get your trusty calculator out and think about a little high school geometry. (A framers Construction Master calculator works great, as it allows input in feet and inches.) Divide the width of the opening by pi (3.14 is close enough) .

The answer is the diameter of a circle whose circumference is equal to the width of the opening. (A lot of carpenters I explain this too begin to get a glazed look in the eye by this point). It is also the height of the arched portion of the opening. If this seems confusing at this point, bear with me.

   If you take a scrap of plywood and cut out a circle of the diameter calculated, your almost there! Next, lean a piece of plywood up in a near vertical position on as flat a surface as possible. Cut a small notch in your circle and draw a line from the notch through the center to the opposite side. Stand the circle up against your plywood with your line as close to vertical as possible and your notch toward the bottom. With your pencil in the notch, roll the circle along the floor while your pencil scribes a line of the ellipse on your sheet of plywood. The result will be a nicely proportioned elliptical arch.