The original painting is 15 x 11 inches as it is facing right side up. The outside dimensions of the mat will be 20 x 16 inches (also facing right side up). In this example, each side of the mat is going to be 3 1/4 wide. That leaves the size of the opening at 14 x 10 inches. This allows the mat to overlap one-half of an inch on each side, top and bottom of the painting. This is enough to adequately cover the painting without having to worry about an edge showing, and I would recommend no less than that one-half inch.
Also, I would like to say that standard size mats can be purchased from a number of retail outlets. The need for a custom mat comes into play when your color choice for a mat is not something sold in stores or when the size of the painting is not something that will readily fit into a standard size mat.
This example shows the entire painting laying on the foam core. I left the photo with more contrast just to show edges and how it looks laid out.
With the painting on top of a piece of foam core cut to the exact same outer dimensions as the outside of the mat (20 x 16). Place your newly cut mat on top of the painting, and make sure that it is placed where you want it when the mat is aligned with the foam core top, bottom and sides. Take a pencil and mark the upper corners on the foam core when the painting is aligned.
Flip the painting up from the bottom (as if it were hinged at the top of the painting, keeping the top of the painting aligned with the pencil marks you just made).
This photo shows the painting attached to the foam core by tape hinges. To make the hinges, cut acid-free framer's tape (or similar product) in four even strips all cut to approximately 3 1/2 inches long. Tape a piece perpendicular across the edge of the painting attaching the painting to the foam core evenly spaced from the right side and from the left side. Attach a second piece of tape adjacent and overlapping slightly each piece of tape. Then cut four more pieces of tape each 4 inches long.
Tape these parallel to the top edge and perpendicular to the tape strips you just adhered. Two are all that are necessary and those two would be to the foam core, but tape seems to fail here in a humid climate, so I frequently use the additional two pieces as shown on the back of the painting.
The first example shows how the painting looks in the finished mat. Of course, the real mat doesn't have all the numbers scribbled on it.
If you want, you can hinge the mat to the frame at the top. Place the mat face down aligned at the top edge (where the hinge will be) of the side with the painting affixed to the foam core right-side up. Place one strip of tape parallel to the top edge, across the joint between the mat and foam core backing. This joint will be on the wrong side of the mat and the right side of the foam core backing.
All that remains is to put the matted watercolor into your frame.