Calculator
Raising a brine that has fallen
The vegetable gives up its water and the brine weakens. This is how much salt puts it back.
Result
136.4g salt
Working
Adding s grams of salt to M grams of brine at c%: (M x c / 100 + s) / (M + s) = t / 100 s = M x (t - c) / (100 - t) = 4.000 kg x (12 - 9) / (100 - 12) = 136.4 g Brine after: 4.136 kg at 12.00%.
Why this needs a calculator at all
The FAO bulletin describes exactly this: the strong brine draws sugar and water out of the cucumbers, which reduces the salinity of the solution, and more salt has to be added to hold it. It also gives the floor - below twelve percent, the bulletin says, the pickles spoil through putrefaction and softening. Adding salt to a brine dilutes nothing, so the arithmetic is not simply the difference.
What this is not
Arithmetic, not advice. It converts the number you type; it does not know what you are fermenting, how warm your kitchen is or whether your salt is pure. Nothing on this page certifies that a preparation is safe, and no result here should be read as a recommendation to ferment at any particular strength. The published parameters, with the sentence each came from, are on the tradition pages, and what can go wrong is on safety.