A pot is a skin
The clay in a thrown form is the wall wrapped round the outside plus the floor underneath, and nothing else. Wrap a 1/4 in skin round the default mug in the form — 3.5 in at the rim, 3.2 at the foot, 4.25 tall — and the shell holds 11.84 cubic inches of clay, of which the wall is 9.26 and the floor is 2.58. At 1.95 g/cm3 that is 378 grams of clay standing on the bat, and 461 grams on the scale before you throw it, once 18 percent is written off to trimmings and to what stays on the wheel.
The floor is doing a fifth of the work there, which surprises most people. A 0.45 in floor under a 3.2 in foot is a solid disc, and it is the part you turn away later.
Shrinkage does not cost you what you think
The page prints a ratio near the bottom that is worth reading twice. At 12 percent linear shrinkage you throw everything 1.136 times oversize to land on a fired target. Clay is bought by weight, weight follows volume, and volume goes as the cube of the linear factor — so that 12 percent costs 46.7 percent more clay, not 12 percent more.
Scaling a range of mugs up by an inch is the same arithmetic and it lands the same way. Everybody prices the extra clay linearly and everybody is wrong by roughly a factor of three.
What comes out of a bag
At 461 grams a ball, a 25 lb bag gives 24 balls with 270 grams left in the bottom, and the clay in one mug costs 89 cents at 22 dollars a bag. Forty mugs is 40.7 lb of clay, so two bags. That is the whole material cost of a mug before glaze, before firing and before an hour of your time — which is the useful context for anyone who has ever been asked why a mug costs what it costs.
Where the model is wrong
It treats the wall as an even thickness from foot to rim. Nobody throws like that. A pot thrown by somebody still learning is fat at the bottom and thin at the top, so the real ball weight runs above this figure; a pot thrown by somebody who has done it for twenty years is closer to even and lighter than the arithmetic says, because the floor gets compressed down thinner than they would guess. Handles, lids, knobs and applied feet are all extra and none of them are in here.
The honest way to use it is as a starting point you then correct. Weigh out what the page says, throw ten, weigh the trimmings, and adjust the loss percentage until the count per bag matches what you actually get. After that it is your calculator rather than a generic one.
Which dimension actually moves it
The page works this out rather than asserting it, because the answer changes with the shape. For the default mug, a sixteenth of an inch added to the wall puts 72 grams on the ball; a thicker floor adds 8; the same sixteenth on both diameters adds 12; extra height adds 6. The wall wins by a factor of six there, and it is also the input nobody has a real number for.
Now flatten the form to a wide shallow dish — 8 in at the rim, 7 at the foot, 2 in tall with a 0.8 in floor — and the ranking inverts. A sixteenth on the floor is worth 68 grams and a sixteenth on the wall only 30, because a floor is a solid disc and its area goes as the square of the diameter. That is why the block is computed for whatever is in the form rather than printed as a rule. Cutting a finished pot in half with a wire settles both numbers permanently, and most potters find the wall thicker than they believed and the floor much thicker than that.
Questions people ask
How much clay does a mug take?
For the shape in the form — 3.5 in at the rim, 3.2 at the foot, 4.25 in tall with a 1/4 in wall and a 0.45 in floor — the shell holds 378 grams of clay, and you weigh out 461 grams to allow 18 percent for trimming and what stays on the wheel. That is about 16 ounces, and 24 of them come out of a 25 lb bag. Add a sixteenth of an inch to the wall and the ball goes up by 72 grams.
Why does a 12 percent shrinkage cost 47 percent more clay?
Because clay is sold by weight and weight follows volume, while shrinkage is quoted as a length. To finish 12 percent smaller you throw 1.136 times bigger in every direction, and 1.136 cubed is 1.467. The extra clay for a size change is always roughly three times the linear percentage, which is why scaling a range up an inch is a bigger order than it looks on paper.
How many pots come out of a 25 pound bag of clay?
Divide the bag by your ball weight and take the whole number. At 461 grams a ball that is 24, with 270 grams left over. The count is set by the ball weight rather than the finished pot, so anything you trim away or leave on the wheel still comes out of the bag — which is why the loss percentage on the form matters as much as the dimensions do.
What density should I use for wet clay?
Your own. Weigh a wedged lump, sink it in a measuring jug to read its volume, and divide. Plastic stoneware bodies sit somewhere near 2 g/cm3, but the figure moves with how wet the clay is and how much grog is in it, and a heavily grogged sculpture body reads differently from a smooth porcelain. The field defaults to 1.95 as a placeholder to replace, not as a fact about clay.
Does this include handles and lids?
No. It is the thrown form only — the wall and the floor. A handle, a lid, a knob or an applied foot is extra clay on top of the ball weight, and a lidded jar is effectively two throwings. Work the lid as its own shallow form if you want it counted, and add the two ball weights together.