Make an Arched Doorway
Lessons from Math Teachers’ Past
By Clint Thomas, Photos by Zoe Thomas
How many of us asked at least once, and probably multiple times during our academic careers, “Why are we learning this? I’m never going to use this.”
I asked the same question quite often in math and geometry classes throughout my schooling. However, it is ironic how often we end up eating those bold words of youth once we enter adulthood and have to deal with the realities of life. This experience recently happened to me while framing an arched doorway for my daughter’s new closet. Framing a door opening, in and of itself, is relatively simple. It requires two king studs, a couple of jack studs, a header, and most importantly, every angle is a right angle. See, we just started with that math stuff that we didn’t need to know—right angles, acute angles, etc.
An arched doorway is simple to frame out once the archway is made. The difficult part of framing an arched opening of any type is drawing out the archway so it will be on the same radius throughout its span. This process involves an excessive amount of geometry to accomplish. Simply put, we have to draw out a rectangle that will serve as the circumference of our arch, then mark out an isosceles triangle inside that rectangle. We then use the sides and the apex of the triangle to determine points beneath the rectangle, strike lines through certain of those points in order to establish the final point that will serve as the base pivot point for the arch. Sounds complicated, right? In actuality, it is quite simple because, just as our high school math teachers tried to explain to us, many mathematical concepts involve formulas. If we know the formula then we can work the problem with ease. The same is true in this case.
To frame an arched opening, begin by taking an exact measurement of the rough opening from left to right. In my project, the rough opening measured 37 inches from left to right. Be sure to measure along the top of the opening in case the studs are not exactly plumb. What might measure 32-3/4 inches at the top may only measure 32-1/2 at mid-level.
Next, it is necessary to determine how “thick” the arch is going to be. In other words, determine the measurement from the top of the rough opening to the top of the finished arched opening. If the archway is too thick, meaning that it hangs down too far, then a tall person will hit their head on it. Most rough door openings are framed to be 6 ft., 8 in. inches high. I framed mine so it is 77-1/2 inches tall. Given the height of the rough opening and taking into account the height of the average person, I decided to design my arch to be four inches thick.