The lye calculation, and how to check one
Updated
Every batch depends on one number, and it is worth being able to verify the calculator rather than trust it.
What a lye calculator does
Every oil has a saponification value: the mass of alkali needed to saponify one unit mass of that oil.
A calculator multiplies each oil's weight by its SAP value, adds the results, and reduces the total by the superfat percentage.
That is all it does. The rest is a units convention and a water figure.
The arithmetic
For each oil: oil weight times SAP value for sodium hydroxide gives the lye required for that oil.
Sum across all oils to get the full-saponification lye weight.
Multiply by (1 minus the superfat fraction) to get the lye you will actually use.
Water is then set as a ratio to the lye, commonly around two to two and a half parts water to one part lye, or as a percentage of the oil weight.
Worked: 500 g oils requiring 70 g lye at full saponification, at 5% superfat, gives 70 × 0.95 = 66.5 g lye. At a 2:1 water ratio that is 133 g water.
Superfat
The deliberate excess of oil left unsaponified, commonly 5%, and it is the safety margin as well as a formulation choice.
It absorbs variation in SAP values, scale error and measurement drift, which is why zero superfat is a lye-heavy bar waiting to happen.
Higher superfat gives a milder, softer bar that goes rancid sooner. Lower gives a harder, longer-lasting, less forgiving one.
Checking a result
Recalculate with a second calculator and compare. They should agree closely; a large difference means one of them has a different oil selected or a different alkali.
Check the alkali: sodium hydroxide for bars, potassium hydroxide for liquid soap, and potassium values run substantially higher.
Check the purity assumption if you are using a potassium hydroxide that is not 100%.
And sanity-check the magnitude: for a common bar recipe the lye is roughly one seventh of the oil weight, so a result far from that is an input error.