Three arithmetic problems, one page
Dye work throws up the same three questions every time. How much powder for a batch, how much solvent to lighten a batch that is too strong, and how much to mix for a job when all you have measured is a test board. None of them is difficult, and all three are easy to get subtly wrong in a way that only shows up when you are halfway across a panel.
Mixing from powder is a straight proportion: an ounce per gallon over a quart is a quarter ounce, which is about 7.1 grams. Weighing in grams is far easier than weighing a quarter of an ounce, which is why the page gives both.
Diluting behaves like the shellac cut
The powder in the jar does not change when you add solvent, so the volume has to grow by the ratio of the strengths. Take 32 fluid ounces at 2 ounces per gallon: that is half an ounce of dye. To make it 1 ounce per gallon the same half ounce has to be in half a gallon, which is 64 fluid ounces, so you add 32. Halving the strength doubles the volume, and going from 3 to 2 grows it by half. It is the same arithmetic as a shellac cut, for the same reason.
What the test board is really telling you
Measure how much dye a sample board took and you get a rate: 1.5 fluid ounces over 2 square feet is 0.75 fluid ounces per square foot, which is 171 square feet per gallon. Multiply by the job area and you have the volume the wood will take, and then you add to it, because the tray and the rag and the jar all keep some.
Twenty five percent extra is a starting point rather than a rule, and it should go up for a job broken into many small parts, up again for open-grained wood that drinks unevenly, and up again for anything where a colour join would be visible. The failure this guards against is specific: mixing a second batch to finish a top, and having it read a shade different under raking light for the life of the piece.
Where this sits
Once the colour is on, the film that goes over it is the film build calculator, and quantities by product type across a whole job are in the finish coverage calculator. If the wood is open-grained and the pores are going to be filled, the grain filler calculator sizes that step. How the surface was prepared changes how dye takes, which is the grit progression calculator.
Questions people ask
How much powder do I need for a quart at one ounce per gallon?
A quarter of an ounce, which is 7.09 grams. A quart is a quarter of a gallon, so the concentration scales straight down. The reason to work in grams is that a quarter ounce is an awkward thing to weigh accurately on most shop scales, while 7 grams is easy, and repeatability is the entire point of measuring rather than eyeballing. Write the recipe on the jar in grams and millilitres and the second batch will match the first.
Why does doubling the dye strength not double the colour?
Because the wood holds a finite amount and the rest wipes off or evaporates. Depth of colour rises quickly at low concentrations and then flattens, and where it flattens depends on the species, how it was sanded and how wet the surface is kept while the dye is on. That is why a sample of the actual wood matters more than any number: two boards from the same tree can take colour differently, and a calculator can size a batch but it cannot predict a shade.
Can I mix a strong stock and dilute it as I go?
That is the usual practice, and the strength mode exists for it. A concentrated stock takes up less shelf space, and every working batch you draw from it starts from the same colour, which is worth more than it sounds when a job runs over several days. What it does not solve is that some dyes settle or change on standing, so shake before drawing and keep the stock labelled with the date and the strength, in the units you actually mixed it in.
How much extra should I mix?
More than you think, and the page defaults to 25 percent as a starting point. The variables that push it up are the number of separate parts, since every part means dye left in the tray, how thirsty the wood is, and whether a colour join would show. For a single tabletop where a second batch would be visible forever, mixing double is not extravagant. Dye powder is cheap next to the cost of stripping a top back and starting again.
Does this work for stains as well as dyes?
The volume arithmetic works for anything you mix to a concentration or scale from a test board, so the dilution and the scaling modes apply to a wide range of colouring products. The powder mode assumes a dry colourant dissolved into a solvent, which is a dye. Pigmented stains are supplied ready mixed and behave differently on the wood, since the pigment sits in the pores and the surface rather than dissolving into the fibre, and thinning them changes how they cover rather than only how dark they read.