There you are: standing at the mouth of a bricked-up hole with a gap that’s begging to be filled. That arch invite precision; it appears as if it were created by the effortless pull of gravity. So plug in your rise (height) and your span (width), and let the calculator above do the rest, spare yourself from guessing about conversions and coefficients. It is the difference between an arch that will last a century and one that sags into gaps between mortar.
First, understand: An arch is always a slice of a circle, not simply a curving line. A flat segmental arch still has a certain radius. And why does that matter? Because you don’t purchase bricks in a random swooping shape. There needs to be center point from which all units spread out.
How to Calculate Your Brick Arch
Enter the width of your opening, and the tool will find that concealed center, then apply the rise (and apply some trigonometry) to figure out what radius might be. With a semicircle, the rise is exactly half of the span, so easy. Most common door and window openings is not as shallow, though. Those are the segmentals. They appear flatter but require more math, since circle they’re part of exists farther out beyond your vision, larger than meets eye.
After establishing the radius, the rest is geometry. With the radius known, the calculator compute the included angle, and then the angle informs you what portion of the entire circle your arch cover. That informs the length of the intrados, or inner arc, on which your brick face will sit. Divide that by the width of a typical brick with a slight mortar joint, and you know how many voussoir you’ll need.
If you choose the keystone rule, the calculator insist on an odd number… Which is crucial. Any other number (i.e., an even one) result in two bricks coming together at the crown, forming a weak vertical mortar line exactly at the top. One keystone sits perpendicularly across from the arc, so it locks the wedge in place. It’s an old Roman trick that still works today, and it’s just that: a tiny bit of structure.
You can see from the output what angle each of those stones should be relative to the next one, that’s the per-brick angle. And if you don’t pay attention to that, you’ll end up with parallel joints. If you use parallel joints different than the correct kind, you will end up with thick mortar on the outside face and no mortar at all on the inside face. That’s bad for shedding water; and looks wrong on the arch itself. Keeping the bricks nice and rectangular keeps the cuts fast and cheap, because you’re cutting the mortar, not the brick.
The calculator shows you the length of the extrados, too, which helps you imagine the difference between the inner curve, and the width of the outer edge. As the depth of the ring increase, or the radius decreases, that gap widens.
Once you have the numbers down, there’s a cadence to the layout of the arch that’s nearly musical: Begin at the outsides and move in toward the middle, with the keystone reserved for last; the last clasp on a bag. This one keeps all the pressure downward and in, pressing it against the abutments. Without this inner locking piece, the outward thrust push outward against nothing but air.
The tool teaches you not to underestimate how much curve a span requires. A six-foot garage arch appears to be pretty flat, until you calculate the angle being formed, which turns out to be quite narrow, requiring each brick to have a slight wedge shape. Mess up on this, and what you’ve got isn’t a smooth arch, but a stack of steps.
Working in brick is a balance between the strengths of the material and the humility required to work within its limitations. With the calculator, you don’t have to worry about the math of geometry. You simply get to enjoy the math of masonry: Measure. Cut. Lay. The math exists solely to make sure the top of the curve closes up perfectly.
That’s no magic, it’s math made to look like masonry. When you set down the last keystone and feel how the whole thing locks into place, you would of understood exactly why all that precision was needed every step of the way.
