A jug of solution is two ingredients
Keeping a made-up alkali solution saves weighing dry alkali for every batch, and it introduces one piece of bookkeeping that catches people out: the solution is carrying water, and that water is part of the recipe whether or not it was counted.
The worked case in the form is a batch wanting 140 grams of alkali at a 33 percent lye concentration, which is 284.2 grams of water. From a 50 percent solution you draw 280 grams to get the alkali, and 140 grams of water arrive with it. The plain water you add is 144.2 grams, not 284.2. Add the full recipe water on top of the solution and the batch has 424.2 grams of water in it instead of 284.2, which is half as much again.
The boundary the page is really about
You can water a solution down. You cannot dry it out. So the strength of your stock is a hard ceiling on the lye concentration of anything made from it, and the ceiling is easy to state: a stock can make a batch exactly when its strength is at or above the lye concentration that batch works out to.
A 50 percent stock reaches any recipe up to a 50 percent lye concentration, which for 140 grams of alkali means anything down to 140 grams of water. Ask it for a drier batch than that and there is no arithmetic to do — the answer is that this container cannot make that recipe. A 25 percent stock is locked out of the 33 percent batch above before you start, and the page says so rather than returning a negative number of grams of water.
Why makers keep a strong one
That ceiling is the whole argument for storing the solution strong. Every recipe below the stock strength is reachable by adding water; every recipe above it is not reachable at all. The cost of a strong stock is that almost every batch needs makeup water weighed as a second step, which is a small nuisance next to keeping a container that cannot make half of what you write.
Where this goes wrong in practice
The strength on the label is a number somebody wrote once, and it drifts. A container left open takes up water and carbon dioxide from the air. A jug topped up from a second batch is at neither the old strength nor the new one. If the label is a guess then every figure here is a guess in exact proportion, and the page has no way to tell.
The other one is volume. A solution is denser than water, the density moves with strength and with temperature, and a measured volume is not a reliable weight of alkali. Everything on this page is a weight.
Named and not explained
Sodium hydroxide and potassium hydroxide are caustic: they cause severe burns and permanent eye injury, and alkali meeting water releases heat. Nothing on this page describes how to make a solution, store one, or handle it. That is not an omission to fill in from context — it is deliberate, and the information belongs to the safety data sheet for what you bought.
Questions people ask
How much masterbatch do I use for a batch?
The alkali the recipe wants, divided by the strength of the stock. At 140 grams of alkali from a 50 percent solution that is 280 grams of solution. The part people miss is the second line: that 280 grams brought 140 grams of water with it, so the plain water for the batch is the recipe water less 140.
Why can a weak solution not make a low-water recipe?
Because the water comes through the door with the alkali and cannot be taken back out. A 25 percent solution carries three grams of water for every gram of alkali; a recipe at a 33 percent lye concentration has room for about two. The page names the weakest stock that could make the batch, which is always exactly the lye concentration the recipe itself works out to.
What strength should I keep my solution at?
That is a decision this page will not make for you, but it tells you what the decision costs: the strength is a ceiling on the lye concentration of everything you can make from it. Whatever number you pick, every recipe below it is reachable and every recipe above it is not.
How many batches does my jug hold?
Jug weight divided by the draw per batch, rounded down. Two kilograms of 50 percent solution at 280 grams a batch is 7 batches with 40 grams in the bottom, which is 14 percent of another draw. The page also reports the alkali and water inside the container, since those are the two things you are really storing.
Can I measure the solution by volume instead of weighing it?
Not reliably. The solution is denser than water, and its density moves with both strength and temperature, so a fluid measure of it is a poor proxy for a weight of alkali. Every figure on this page is a weight for that reason.
Does the strength on my container stay accurate?
It drifts. Alkali solutions take up water and carbon dioxide from the air once opened, and a container topped up from a fresh batch sits between the two strengths. This page multiplies whatever strength you enter and cannot detect a stale label, so the arithmetic is only as good as that number.