Mitering Curved to Straight Mouldings

When an arc joins a straight line, some thinking and fussing are required to get a close match. Here, finish pros discuss the fine points. August 24, 2005

Is there a good way of figuring out the angle for joining a round to a straight molding like this in such a way that the detail matches? Any help is appreciated.

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Forum Responses
(Architectural Woodworking Forum)
From contributor K:
For situations like this, I simply place the straight moulding on the wall in it's final location and trace around it with a pencil. Then I remove the straight moulding and do the same with the radius segment. I then transfer the intersection of the lines on the wall to the edges of the radius moulding. I remove the radius piece and place the straight piece back on the wall and transfer the intersection of the lines to it as well, and just connect the lines on each piece and cut to the lines. You should be in good shape and the profiles should match perfectly.

From contributor J:
Here is a suggestion. As you have it laid out draw both inside and outside lines of your curve and extend them beyond that intersection, do same thing with the straight piece. You now have overlapping lines from each piece. Draw a line through them from the outside corner through the inside corner. That will give you the angle needed, and just use a bevel square to copy it and transfer to your saw.

From the original questioner:
What I'm trying to say is that if I cut the molding as you describe the details won't match. Or maybe I’m not understanding things? This drawing shows that the lines are concentric to the circular molding and in the same distance from the edges as the straight molding but they don't match.

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From contributor R:
This is an interesting problem and an excellent drawing to clarify it. By looking at the drawing it looks like you’re not cutting an angle but a set of curves that cope together. The solutions are dependent on how many of them you’re planning to do. If you’re only planning on doing one, draw it out to scale and map out the intersection points and use that as a template to cut both sides of the miter and fit from there.

From contributor D:
The ideal is to (machine) cope the end of the curved piece to fit into/over the straight, if the profile will allow this. If it is an astragal or similar profile, the curved piece can still be coped, and then the straight piece can be profiled on the outer edge (coping saw, carved) to match the intersecting curve.

The reason straight miters resulting from the overlapping of the two molds doesn't work is due to the changing shape of the profile as it curves past the straight piece miter - by the time you get to the outside tip of the curve, it has curved away from the line established at the inside of the joint, hence the banana.

Another strategy is to make the curved mold straight at the point that the miter begins - if it won't be obvious. In practice, we just adjust the miter to where we can easily sand/carve the difference and go with it. This is what we do almost daily. It does help if you can design the molding to help minimize this dilemma.

From the original questioner:
It looks like the banana cut is the way to go as shown below.

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From contributor P:
I deal with this situation all the time when mitering curved to straight. The tighter the radius or the wider the profile increases the problem. You always end up with some type of a curve at the joint instead of a miter. I usually use a pair of scraps to mock up the intersection using a stationary disk sander and a spindle sander. I then transfer this info to some 1/4 mdf template stock. I can then cut with confidence.

From contributor L:
Would the joint between the curved and straight moldings be the same radius as the individual details on the curved molding? If so, it would be easy to use a trammel and router to cut male and female templates for the midline radius and use those with a template bit to get a near perfect fit.

If you standardized on several lengths for the curved molding, you could go one step further and make a 4-cut jig set (L&R x Straight and curved) for each length so there would be no thinking required during the installation.

From contributor C:
We run into this problem a lot. Sometimes the difference in details where the curved meets the straight are close enough to blend in by sanding, which you probably already know. For the ones that are not within sanding room, the curved cut is the best way we have found to get the details to meet.

I have not seen a formula for this, but I would like to. One true arc from the inside corner of the miter to the outside corner does not intersect exactly everywhere that the details within the moulding come together. We find one that is the closest and requires the least amount of sanding, and go with that. If it is still severely off, we cut different arcs, or lines, along the miter that do intersect well at the details. For both ways we sometimes do it on the CNC router.

From contributor F:
There is no math formula, but when a straight section of molding meets a curved section of molding with the same profile a curved line is needed at the joint to match up the various aspects of the two.

This curve is obtained by drawing the two at full scale in their respective relationships to each other and drawing their various elements such as steps, etc. If there are large unbroken areas draw a series of evenly spaced parallel lines in those areas in exactly the same locations with regards to the moldings edges in both the straight and curved sections.

Now connect these points with straight lines. The resulting curved dotted line is the curved miter that will bring the best results. You can use a compass trial and error until you get a setting as close as possible to the dotted line.

From the original questioner:
I ran the molding and it worked fine. All I did was use a simple cad program and using the three point circle tool to get a true arc that hit the critical points. I guess a spline may be necessary on a different detail. I used CNC, but you could also just print out the drawing full scale.

From contributor A:

I see that the joint cannot be straight or curved in this case. It is actually a zig-zag of several straight lines. The angles of which vary from point to point with the various radii of the forms in the moulding when as in this case the radii are not equally spaced. A spline generated using a Cad program is close but no banana, as they say.

The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).

Comment from contributor H:
So here’s my spin on it. I used layout board (similar to the back of a note book, comes in 4x8 sheets) to make templates of each curve and intersecting leg, laid them out and made a corner to corner cut. Taped the joint together laid it on top of another piece of layout board, tacked it to a scrap of ply and cut out the footprint of the corner. I then cut slices of the moulding, traced their profile onto the template and ran the high points of each detail using a compass as a scribe.

Then as described in the drawings and articles above, intersected the points and cut it with a very sharp utility knife. If it's a little dull it will tear the card board, so lots of fresh blades on hand. I then took them and traced them in pencil onto 1/4 MDF, then I cut off the waste and cleaned them up on a spindle sander. I made the template oversized on the back of the molding and past the front edge of the joint to accommodate the base of my trim router.

I turned the molding over and placed the template on the back and tacked it with a micro-pin nailer, clamped it to the table, trimmed the waste with a jigsaw, leaving 1/16 and trimmed it with my router and viola - a perfect miter.