The rail is longer than the frame size, and by how much is the profile
Every rail on a mitred frame is measured along its long point, the outside edge, because that is where the saw meets the stock. What has to come out right is not the outside but the rabbet, which sits back from the outside edge by the face width less the lip.
With the defaults here — a 1-1/2 inch face and a 5/16 lip — that setback is 1-3/16 inches, and it happens at both ends of every rail. So a rabbet of 16-1/8 needs a rail 18-1/2 long on the outside. Cut that rail at 16 inches, which is what the frame is called, and the rabbet comes out at 13-5/8. The mat will not go in and the moulding is gone.
The identity worth carrying away is the other one: outside = sight + twice the face width. On the defaults the sight opening is 15-1/2 by 19-1/2 and the outside is 18-1/2 by 22-1/2, which is exactly 3 inches larger in both directions, and 3 inches is twice the 1-1/2 face. Move the lip in or out and the rabbet slides between them without touching that relationship.
Slack in the rabbet, and what it costs you at the sight edge
The rabbet is cut a little larger than the package so the glass, mat and backing drop in rather than needing persuasion. An eighth of an inch across the whole dimension — a sixteenth each side — is a common bench figure and it is the default here.
That slack comes straight off the lip. The moulding overlaps the package by the lip width less half the slack, which on the defaults is 5/16 less 1/16, or a quarter of an inch on each edge. That quarter inch is board the viewer never sees, and it has to be added to the mat border you designed rather than subtracted from it. Design a 2-3/4 inch mat border and the visible border is 2-1/2 once the moulding is over it.
Push the slack up and two things happen at once: the package rattles, and the covered strip narrows until the lip is barely holding anything. The page flags the case where the slack is as wide as the lip, because at that point the rabbet is no longer gripping the package at all.
Sticks, offcuts and why chop is not always the expensive option
One 16 by 20 frame in the default profile takes 82 inches of moulding — 6.83 feet — plus the saw loss, and an 8 foot stick has 94 usable inches once an inch comes off each end. So one frame comes out of one stick with 10-1/2 inches left, and that offcut is worth nothing until a job turns up wanting a piece that short in that exact profile.
The packing in the page is first-fit-decreasing: long rails placed first, each into the first stick with room. That is what a person does at the saw. It is a heuristic rather than a guaranteed best packing, and on a run of one repeated size it lands on the same answer you would get by hand. Where it gets interesting is at a mix of sizes, because the short rails then fill the tails that the long ones leave.
Weigh that against a chop service, which cuts the four rails to your numbers and charges you for the footage in the frame rather than the footage in the stick. On a single frame in a profile you will not use again, chop usually wins outright. On a run of the same size, cutting your own wins as soon as the second frame starts fitting into the tail of the first stick.
The pair matters more than the number
A frame closes when opposite rails match each other, not when they match your tape. Four rails cut a sixteenth long assemble into a frame a sixteenth big, which nobody will ever notice. One rail an eighth longer than its opposite twists the whole frame and opens the two mitres at the far corner, which everybody notices.
So cut both members of a pair in the same setup without moving the stop, and check the second against the first rather than against a rule. The same applies to the angle: a saw a quarter of a degree off 45 leaves a gap you can see at every corner once the four errors accumulate, and it accumulates fastest in a profile with a wide flat face.
What this page does not cover
Anything that is not four rectangles. Hexagonal, octagonal and other polygon frames need a different mitre and are handled on the miter angle page. Stacked mouldings, where a second profile is fitted inside or behind the first, need each layer worked separately with the inner layer treated as the package for the outer one — run the page twice.
Nor does it settle joining. Whether the corners take vee nails, splines, dowels or nothing but glue and a strap is a decision about the profile, the equipment on the bench and how the piece will be handled, and it has nothing to do with the arithmetic here.
Questions people ask
Why is my rail longer than the frame size?
Because a rail is measured on its long point, the outside edge, and the rabbet sits back from that edge by the face width less the lip — at both ends. On the default profile that setback is 1-3/16 inches per end, so a 16-1/8 inch rabbet wants a rail 18-1/2 inches long. Cutting the rail at the nominal frame size gives a rabbet of 13-5/8 and a frame that will not take the mat. Every frame arithmetic error people make is some version of this one.
What is the difference between the rabbet size and the sight size?
The rabbet is the step the package drops into and it is the number the mat and glass are cut to. The sight is what you can see once it is assembled, and it is the rabbet less twice the lip because the lip covers that much of the package on each side. On the defaults the rabbet is 16-1/8 by 20-1/8 and the sight is 15-1/2 by 19-1/2. Frames are usually sold by rabbet size but photographed by sight size, which is why a frame often looks smaller in the flesh than it did in the listing.
How much slack should I leave in the rabbet?
An eighth of an inch across the whole dimension, so a sixteenth each side, is a common bench figure and is what the field defaults to. It is not a standard and nothing here says it is. Less than that and the package needs persuading in, which is how glass gets broken during fitting; more and the package rattles and the lip stops covering enough of the edge to hold it. The page flags the point where the slack has grown as wide as the lip, since the rabbet is not gripping anything past there.
Is cutting my own moulding cheaper than buying chop?
Only once the offcuts get used. One 16 by 20 frame in the default profile takes 6.83 feet and leaves 10-1/2 inches on an 8 foot stick, and that offcut is worth nothing until a job comes along wanting a short piece in the same profile — which in framing is rarely. A chop service charges roughly for the footage in the frame instead of the footage in the stick, so on a one-off in a profile you will not repeat, chop generally wins. On a run of the same size it flips quickly.
Does this work for a frame that is not a rectangle?
No. Everything here assumes four rails and eight 45 degree mitres. A hexagon, an octagon or any other polygon needs the mitre angle worked from the number of sides, which is what the miter angle calculator does, and the rail lengths then come off the polygon geometry rather than off two dimensions. Stacked mouldings are also outside it, though you can get there by running the page twice and treating the inner frame as the package for the outer one.