The pore is a volume, not a surface
Filling grain is a volume problem dressed up as a surface one. Take a flatsawn open-grained face where the pores run 3 mils deep and cover about a quarter of the surface. Each square foot is 144 square inches, so the pore volume is 0.003 inches times 0.25 times 144, which is 0.108 cubic inches per square foot. Over a 40 square foot job that is 4.3 cubic inches, or about 2.4 fluid ounces of actual solid material. That is the target, and it is much smaller than the amount of filler you will get through.
Solids decide the pass count
Here is the part that surprises people. Press filler into a pore until it is level and the pore is full of wet filler, not full of filler. A product at 40 percent solids leaves 40 percent of that volume behind and the remaining 60 percent evaporates, so the pore is 40 percent filled and 60 percent still open. The second pass fills 40 percent of what is left, taking you to 64 percent. The third reaches 78, the fourth 87, the fifth 92, the sixth 95.
That is a geometric series, which means it never reaches 100 and the later passes buy less and less. Raising the solids is worth far more than adding passes: at 60 percent solids the same 95 percent fill takes four passes instead of six, and at 80 percent it takes two.
Why you buy so much more than the pore volume
Filler is applied across the whole surface and most of it is squeegeed straight back off. Only what goes into the pores stays. Over six passes the wet volume pressed into the pores of that 40 square foot job comes to about 5.7 fluid ounces, and the default 150 percent surplus takes what you should have on hand to roughly 14. That is not waste in the sense of a mistake, it is how the process works, and running out mid-panel is worse than the surplus.
Where this sits
Once the pores are level, the film goes over the top, and how many coats that takes is the film build calculator. If the wood is being coloured first, the dye mixing calculator sizes that batch, and a sealer coat between colour and filler is often a shellac cut. Sanding the filler back is where a schedule loses time, which the grit progression calculator covers, and the whole thing is an argument for a finishing schedule laid out in advance.
Questions people ask
Why does one pass of grain filler never fill the grain?
Because what you press into the pore is mostly liquid. A filler at 40 percent solids by volume leaves 40 percent of what went in and the rest evaporates, so a pore packed perfectly level dries back to 60 percent open. Nothing has gone wrong and no technique fixes it: the only levers are a higher solids product, more passes, or accepting a partly filled pore and letting the film finish over it carry the difference.
How do I estimate pore depth and the open pore share?
An offcut of the same board under a raking light tells you more than any table, and a loupe helps. What matters is that both figures are properties of the actual wood in front of you rather than of the species name, since a flatsawn face shows long open pores and a quartersawn face off the same log shows short ones at a completely different density. If you are unsure, run the page twice with a low and a high estimate and see whether the answer changes in a way that matters.
Is a higher solids filler always better?
It reaches a given fill in fewer passes, which is the whole advantage, and it costs you elsewhere. A stiffer, higher solids product is harder to press fully into a deep pore, harder to squeegee off cleanly, and more likely to leave residue on the surface that shows up under the finish. Which product suits which surface is a question for the manufacturer and for a sample board, and this page takes no position beyond the arithmetic of what shrinks.
Can I just use more coats of finish instead of filling?
Many schedules do exactly that, and the arithmetic explains when it works. Filling a 3 mil pore with film means building at least 3 mils over the whole surface and then levelling it flat, which is a lot of coats and a lot of sanding, and the levelling is where cut-through risk comes from. For shallow pores it is a reasonable route. For deep ones the filler is doing in a few passes what the film would need many coats to do.
Does the calculator assume the filler shrinks straight down?
Yes, and that is a simplification worth knowing about. The model treats each pass as filling the open volume and drying back to its solids fraction, which is the dominant effect. It ignores that filler can bridge a pore rather than fill it, that it can sink further over the following days, and that some of what looks filled at the end of a pass is surface residue rather than pore contents. Those all push in the same direction, which is that the real pass count is at or above what the page reports rather than below it.