by Michael Sloggatt
I can remember sitting in trigonometry class in high school,
thinking, "When am I ever going to use this?" But in fact, many
construction problems can be solved by using basic math.
One of my recent projects, for example, featured a curved wall
that needed crown molding. While made-to-order flexible crown
is an option, in this case the match wasn't perfect, and I
needed only about 2 feet to finish the wall.
Not wanting to waste 10 feet of expensive custom crown (the
minimum order was 12 feet), I decided to cut straight sections
of crown into wedge-shaped segments and glue them together to
form an arc that would fit the curved corner.
Calculating the Layout
First, I needed to determine the radius of the arc (or corner).
With a long straightedge placed along each wall, I drew
extension lines on the ceiling and measured the length from the
starting point of the arc to the intersection point of the
extension lines (see "Determining the Corner Radius," ). Then I
measured the distance from the intersection point of the
extension lines to the corner.
With the help of Pythagoras' very useful theorem (c2=a2+b2) and
a little bit of geometry, I used these measurements to
determine the arc's chord length (x) and rise (y), which I
needed for calculating the arc's 9.47-inch radius.
Once I knew the radius of the arc formed by my curved corner, I
could determine the exact size and shape of the wedge-shaped
segments of crown molding. Each crown segment would need to be
angled on each side to form the arc; the shorter the segments
were, the more "rounded" the faceted crown would appear to be.
I decided a workable length for each segment would be 3/4 inch
each (as measured from short point to short point on the back
of the crown).
To determine the cut angle for the sides of the crown segments,
I drew another right triangle, with 9.47 (the length of the
arc's radius) representing the side adjacent to the central
angle and half the length of the 3/4-inch-long crown segment
representing the side opposite that angle (see "Cutting the
Then I used the tangent function to find the angle, which I
looked up in the trigonometry table in my handy Pocket Ref (by
Thomas J. Glover; Sequoia Publishing), a great reference guide
I found at my local hardware store. This angle measured a
little over 2 degrees.
Determining the Corner
To make a section of curved crown for a rounded outside
corner at the intersection of two perpendicular walls,
the author first had to figure out the exact radius of
the wall plane. He projected the 90-degree outside
corner onto the ceiling, then used math to calculate
Cutting the Crown
After calculating the curved wall's 9 1/2-inch radius,
the author turned his attention to the crown segments,
which he decided to make 3/4 inch long at the base. He
used trigonometry to find the proper miter angles, then
cut the segments to length and fastened them together
with glue and brads.
Putting Together the Pieces
Now it was time to make some sawdust. When cutting standard
crown on a miter saw, the crown is always cut upside-down and
backward, so I measured the 3/4-inch length of each segment
along the base of the crown. I made the first (left-hand) cut
and marked the crown's length, then reset my saw for the
After fastening the glued-up length of
curved crown in place, the author installs the remaining
sections of straight crown and applies a paintable filler
(top). A vigorous hand sanding helps fair the filler and
individual crown wedges (middle), giving the trim a smooth
Once all the segments were cut out, I applied glue and fastened
them together piece by piece, using 1-inch brads in my nailer.
After the glue set up, I fastened the curved section of crown
to the wall and finished installing the adjacent pieces of
By using a paintable filler, MH Ready Patch (Zinsser Co.,
732/469-8100, www.zinsser.com), and giving everything a
good sanding, I was able to make the crown curving around the
corner look as if it were carved from one piece (see photos,
The project took about 2 hours from start to finish.Michael Sloggatt Jr. is a carpenter who
works in Farmingdale, N.Y.