The company I work for builds spec homes. One of the ways we
dress them up is by adding barrel-vault ceilings. Except for
the layout, these impressive architectural details are not that
hard to frame. A carpenter and helper can do it in four to five
Our vaults are typically installed in a rectangular opening in
a hallway or master bathroom. As a result, the opening is
rarely more than 6 feet wide or 12 feet long. Framing a larger
vault wouldn't be any different, but we've never had the
Geometry of a Barrel Vault
The surface of the barrel is part of the inside surface of a
cylinder; a section through it is an arc of a larger circle.
The ends of the vault can be plumb and flat, or curved like the
barrel itself. We usually make them curved.
Like a hip roof. The layout for this
kind of barrel is similar to that of a regular hip roof —
one where all the pitches are equal. On a hip roof, common
rafters run up from the sides and meet at the ridge. On a
barrel vault, half-arc segments run up from the sides and meet
at the high point of the vault (see Figure 1). If the vault is
small enough, you can make the entire segment from a single
piece of plywood.
Figure 1.The vault framing (top) consists of
radiused plywood "rafters" at the sides and ends, and
elliptical plywood "hips" at the corners (drawing, middle).
Two-by-four "purlins" run between the plywood pieces. The
surface is finished later with a double layer of 1/4-inch
A hip roof has a single common rafter, called the king common,
at each end. The king common runs from the top plate to the
ridge board. The same is true of a barrel vault except that the
end piece is half of an arc segment, and instead of hitting a
ridge it meets the midpoint of the last full arc segment in the
The hip is an ellipse. The vault framing also includes hiplike
pieces that come in from the corners at 45-degree angles. In
plan, they look exactly like hips, but from the side you can
see they're curved. Because they're formed by the 90-degree
intersection of two cylindrical curves, their shape is actually
The first step in framing a barrel is to create an opening for
the vault to go into. If it's on the top floor, we'll cut out
some ceiling joists and head off the opening. That may not be
possible on a lower floor, in which case we'll drop the
surrounding ceiling by framing in a soffit (Figure 2). The size
of the opening might be specified by the designer; if not,
we'll come up with a size that seems proportionate to the room.
In the project photographed for this article, we framed the
opening about 12 inches off the main walls of the room.
Figure 2.On upper floors, the opening for a barrel
vault can be created by heading off ceiling joists (top). In
rooms with high ceilings, the vault may fit in a dropped soffit
After the opening is framed, we double-check to make sure it's
square and the sides are reasonably parallel. Then we measure
the distance across the opening at several points and use the
average distance to determine the curves for the barrel.
Determining the Radius
Once we know the size of the opening, we decide how tall the
vault should be at its highest point, then calculate the radius
required to hit both edges of the opening while passing through
the high point. To put it mathematically, we know a chord
length (the width of the opening) of a given circle, we know
the plumb distance from the center of the chord to the
circumference of the circle (the height of the barrel), and we
need to find the radius of the circle.
The easiest way to get the answer is to use a construction
calculator that has a trig function. I use the Construction
Master Pro Trig Plus III. For the vault shown in this article,
which is 48 1/2 inches wide and 12 inches high, I punch in the
48 1/2-INCH RUN
The screen displays the radius of the arc, in this case 30 1/2
inches. You can also use algebra to calculate the radius
If the width and the height of a barrel
vault or segmental arch are known, you can use this formula to
calculate the radius of the curved arch
Making Arc Segments
We make the arc segments out of plywood. You could use OSB, but
that would make it harder to see the layout and make clean
cuts. Whenever possible, we try to gang-cut the pieces with a
jigsaw (Figure 4). We then cut one in half to make the king
commons for the ends.
Figure 4.The blanks for the arc segments are as
long as the opening is wide. After marking the radius on the
top piece (top), a carpenter cuts three arcs at once
Laying Out the "Hips"
The first time we framed this kind of vault, we didn't fully
understand how to lay out the ellipses. When our initial
efforts failed, we installed the segmental arches, or
"commons," then scribed the ellipses by taping a pencil onto a
4-foot level and sliding the level along the plane of the
barrel to mark the shape onto an oversized piece of plywood
that had been inserted where the "hip" was to go. The method
worked, but it was time-consuming and the curves weren't as
fair as they should have been.
The next time around, I called Joe Fusco, a cabinetmaker I know
in New York, to ask what we were doing wrong. He sent me a
drawing that explained how to lay out the ellipses; without it
I'd probably still be tracing the curves.
There are two numbers you need to know to lay out an ellipse:
the length of the major axis and the length of the minor axis.
If you have these numbers, you can also locate the two focus
points. Once you have those points, all it takes is some
picture-hanger wire and a pencil to draw the curve (see "Laying
Out the Elliptical Hips").
In a vault of this type, the minor axis matches the diameter of
the cylinders from which the barrel is formed. Since we needed
to draw only the top half of the ellipse, we used half the
diameter, the radius of the circle — 30 1/2