Summarize:

Coping a corner involves installing one piece of crown molding flush with the wall with the second piece laid on top. This is done by mitering one corner and then using a coping saw to cut the wood behind that corner out. Since this method requires the use of a manual tool, it can be kind of tricky to cut the back of each piece out. The seam between the 2 pieces of molding will be cleaner, though. The amount of time it takes for you to cope a corner is entirely dependent upon how comfortable you are with a coping saw. For professionals, this may take 10-15 minutes. If you aren’t familiar with a coping saw, this may take you a little longer. To cope a corner, you’re going to install one piece of crown molding on top of another. The piece on top is the one that you cope to fit on top. Start by using a miter saw to cut one piece at an angle as described in the previous method.  This is the best method if your walls aren’t perfectly square or your home is older. It’s also more forgiving, since there’s only one cut involved. Since you’re not actually matching 2 pieces together, it’s not important that your cut is accurate. You can always make minor adjustments with your file. The matching piece does not require coping. You only need to make a perpendicular cut to make it flush with the wall. You can do this with a miter, coping, or circular saw. To ensure that you don’t accidentally remove a piece that you need, take a pencil and run it along the face of your crown molding where it meets the corner. With the edge highlighted, you’ll have an easier time keeping your cuts accurate. This will keep you from accidentally cutting into the top of the crown molding. You only need to remove the back. Take your crown molding and place it on a stable work surface. Adjust the piece so that the edge you’re going to cut is hanging 8–12 inches (20–30 cm) over the edge of your work surface. Use c-clamps or table clamps to hold the crown molding in place by wrapping the clamps around the table and the molding. If you’re really experienced with a saw, you can simply hold the molding down with your nondominant hand while you cut. With your crown molding secured, place the blade of your coping saw directly under the face of your crown molding. Carefully move the saw back and forth at a 45-degree angle to begin removing the wood behind the molding. Work the saw all the way through your crown molding and remove the wood in the back.  Your cut doesn’t need to be exact since you’re going to use a file to make your cut flush. In other words, you’re cutting towards the center of your crown molding and removing the wood behind it. Continue to use your coping saw to cut through the wood. This can be kind of awkward to do since you need to move the saw while you cut. Work slowly and adjust the angle of your saw as needed to trace behind the face of the molding. For some people, it’s easier to work in smaller sections by making vertical cuts into the back of the crown molding. This makes the pieces that you’re cutting more manageable. With most of the wood behind the crown molding gone, there is still going to be 1–5 millimetres (0.039–0.197 in) of wood that you can’t accurately remove with your coping saw. To remove this wood, place a file underneath your crown molding. Brace the top of the crown molding with your nondominant hand. Rub the file back and forth along a section until you’ve worn most of the wood away. Repeat this process for every other section that needs to be trimmed. Don’t run the file back and forth so quickly that you snap the crown molding. If you do, you’ll need to cut a new piece. Coping a joint is more of an art than a science, and you may need to file away more wood. To see how your joints fit, hold your 2 pieces together at a 90-degree angle where you’re installing them. Place the uncut piece underneath the coped joint. As soon as the 2 pieces are flush, you’re done!  If the angle is correct but the joint won’t sit flush, you need to continue to remove wood from the back of your piece. Use silicone caulk to fill in any gaps after you’ve installed your crown molding.
Plan to spend 10-15 minutes coping your corners. Cut one of your pieces of crown molding to match the angle of your wall. Outline the edge of the corner that you’re going to cope in pencil. Clamp your crown molding to your work surface. Cut through the back of your crown molding with a coping saw. Remove most of the wood behind the end that you’re coping. Use a file to remove the smaller sections near the face of the crown molding. Hold your 2 pieces together to see how the coped joint fits.