Two right answers that disagree
Take the default mould: an 8 inch bowl, 2.5 inches deep, with half an inch of overlap on the rim. The curve it describes has a radius of 4.45 in, the profile from rim to rim across the bottom runs 9.94 in, and adding the overlap gives a developed profile of 10.44 in. The surface of that dish is 69.9 square inches and the flat shelf adds 6.5, so 76.4 in all — and a disc with 76.4 square inches of area is 9.86 in across.
Half an inch apart on an eight inch mould, which sounds like nothing until you look at what it is. A 10.44 in disc has 85.7 square inches in it against a surface of 76.4, so cutting to the profile brings 12 percent more glass than the mould has room for. Cutting to the area instead leaves a line across the blank 0.58 in short of reaching the rim.
Where the surplus goes
It is not a modelling error, it is what a disc is. Area grows as the square of the radius and the profile grows as a line, so no flat circle can match a curved surface in both length and area at the same time. Something has to absorb the difference. In a shallow slump it disappears into a slightly thicker rim and nobody ever notices. In a deep one it shows as a wave round the edge, or the blank rides up the wall instead of settling, or the glass thickens where it has nowhere to go.
The depth block on the page makes the trend visible. On the same 8 inch bowl the gap between the two diameters is 0.15 in at 1.25 deep, 0.58 in at 2.5, 1.24 in at 3.75 and 2.07 in at 5. It is not far off quadrupling every time the depth doubles, which is why deep drops are a different craft from shallow dishes rather than the same one done further.
The thickness line, and what it is worth
A 12 in blank at a quarter inch has 113.1 square inches against the mould surface of 76.4, a ratio of 1.48, so mass conservation says the finished piece averages 0.37 in. That average is real in the sense that the glass has to go somewhere, and useless in the sense that no slumped piece is an even thickness. It is thin where it stretched and thick where it sat, and the difference between those two is often larger than the average change.
Use it as a check on the size of the blank rather than as a prediction of the wall. A ratio of 1.48 already says the 12 in blank is bigger than either of the two sizes the mould asks for, and if it comes out near 2 you are cutting a great deal more glass than the mould has room for.
Drop rings behave differently
A drop ring is the one case where the depth is not a property of the mould at all. The ring only sets the hole; how far the glass goes down is a decision made with the schedule and the heat work, and the same ring gives a shallow bowl or a tall vessel depending on how long it is held. Putting an intended depth into the page tells you what blank that intention needs, but the page has no way of knowing whether the schedule you run will produce it, and the honest answer to how far a given glass drops in a given time is a test piece rather than an equation.
The ring case also carries the biggest thinning, for the obvious reason that the glass has to stretch to get there. That is arithmetic anyone can follow and it is still not a prediction of where it will thin.
Questions people ask
What size blank do I cut for a slump mould?
There are two defensible answers and the page prints both. For the default 8 inch bowl 2.5 in deep with half an inch of overlap, the profile blank is 10.44 in and the equal-area blank is 9.86 in. The profile one reaches the rim with glass to spare; the area one has exactly enough glass but has to stretch to get there. Which you want depends on whether you would rather trim a rim or accept a thinner wall.
Why do the edges of a deep slump wrinkle?
Because a flat disc big enough to reach the rim of a deep mould has more area than the mould surface holds, and the surplus has nowhere to go but sideways. The page prints the two diameters and the gap between them, and the gap grows fast with depth — on an 8 inch bowl it goes from 0.15 in at 1.25 deep to 2.07 in at 5 deep. It is geometry rather than a fault in the firing.
How much does glass thin when it slumps?
On average, by whatever ratio the blank area bears to the mould surface — a 12 in blank on the default mould averages 0.37 in from a 0.25 in start, because the blank is half again bigger than the surface. But glass never thins evenly. It is thinnest where it stretched most, usually part way down the wall, and near its original thickness where it sat on the bottom. Treat the average as a size check, not a prediction.
How deep will glass drop through a ring?
That is set by the glass and the schedule, not by the ring, and this page does not attempt it. The depth field for a drop ring is your intention rather than a measurement, and the page tells you what blank that intention would need. How far a given glass actually goes in a given hold is a question for a test piece and for whatever your own firing log already says.
Does the profile include the overlap on the rim?
Yes. The allowance is added to the diameter, so half of it lands on each side, and the flat shelf it creates is counted in the surface area as well as in the length. If you enter it as a radius by mistake the blank comes out half an inch small, which is exactly the sort of error that only shows up after the glass is cut.