You don't understand significant figures.
D@mn dyslexia 0.40 or 0.04 I usually catch those errors but I missed it this time.
Link 1: cups, quarts, gallons, liters, and (g = mL), which as I pointed out is incorrect depending on your level of precision.
Link 2: liters or quarts.
Link 3: says to use w/w but then immediately says to use w/v in the next newer article:
https://sciencing.com/make-five-percent-solution-salt-8076940.html
Link 4: cups.
They overwhelmingly measure water by using volume.
1 g = 1 mL is also correct depending on your level of precision.
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Mine currently is what is practical and helpful for someone on this forum to make use of in their endeavor to mix up a safe lacto-ferment brine.
I included link 3 and the link to Purdue University to show that the % weight formula I am using is accepted in the scientific and chemistry communities as an appropriate way to calculate the % concentration of a solution.
My previous understanding of % volume concentration was with only liquids involved; as explained in this article.
https://www.thoughtco.com/calculate-volume-percent-concentration-609534
Thank you for showing me another method to calculate the % concentration. I will come back to this in a bit.
I didn't say that the measurements were not by volume. I stated the calculations were by weight. In all of these calculators if you convert the volume of water to grams at 1 g/mL and select grams for the measurement of salt you will readily see that the calculations are by % weight and not by % volume.
However, after further review I see that these calculators are using a different third formula entirely.
For reference 1 gallon of water weighs ~3785 grams.
Link 1 for a 10% 1 gallon solution 378.5 grams salt
Link 2 for a 10% 1 liter solution 100 grams salt - selecting gallons gives salt in ounces
Link 4 for a 10% 1 gallon solution 379 grams salt.
Deconstructing this their "Web Formula" seems to be: gram Salt = gram Water * % salt.
This leaves us with 3 different ways to calculate the salt needed for a particular concentration of brine.
For the following:
"W" is the weight of water
"V" is volume of water in mL
"X" is the percent concentration of salt
"S" is the weight of salt
2.17 is density of salt in g/mL
Answers below are for 1 gallon and 5% salt are and are shown to the nearest gram.
% Weight Method
S = (W / (1 - X)) - W
S = 199 grams = 35.03 teaspoons = 1/2 cup + 3 Tablespoon + 2 teaspoon
% Volume Method
S = (2.17 * V * X) / (2.17 - X)
S = 194 grams = 34.06 teaspoons = 1/2 cup + 3 Tablespoon + 1 teaspoon
% Web Method
S = W * X
S = 189 grams = 33.27 teaspoons = 1/2 cup + 3 Tablespoon + 1/4 teaspoon
If you use work these equations backwards from say 1 gallon water and 194 grams salt the % concentrations are:
4.88% for % Weight
5.00% for % Volume
5.13% for % Web
These are all safe concentrations of salt for a lacto-ferment brine. Regardless of the method one uses you should get a safe ferment. 5.13% is a bit on the high side but some vegetables such as olives call for up to 10% salt. The biggest difference in the final product will be taste and possibly crunchiness but with good notes the salt levels can be adjusted on future batches.
After all this I am still left with one un-answered question. What is the method used by the folks who came up with the safe range of 2%-5%? I have yet to see a definitive answer on this.
One could split the difference and use the % volume method that
@RPh_Guy has laid out but for or now I will continue to use the % weight method. Pick one that you are comfortable with and go for it.
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