- Thread starter Spice
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Depends on how you set up the problem, but yes, you could use this conversion. I re-created the "0.40 rule calculations" a couple of years ago and figured out that someone decided to design a hypothetical soap recipe made with "full water" and a typical superfat. They calculated the volume of soap batter made with that recipe, and correlated this volume with the weight of the oils in the recipe. Factors involved are the density of water and the density of oil, and assumptions about superfat %, water content, and such.

Why would some people use 0.39 (or other number) rather than 0.40? Simple -- this rule is accurate only if the assumptions used to create this rule are followed. It will not be as accurate if the assumptions are not met. The 0.40 rule doesn't account for recipes made with more concentrated lye solution (aka a water discount). This means the level of soap in the mold will be lower if you use a "water discount" rather than "full water". The rule also doesn't account for any additives that add a lot of bulk to the soap -- salt, oatmeal, food purees, exfoliants, etc. A soap batter with bulky additives will fill the mold higher than expected.

my apologies for not being clear on this question, I believe I misled this thread, what I was referring to, and your reply was brilliant in respect to the water discount by the way; I was referring to the calculation that is made when figuring the volume for a soap mold. For example lxwxh, then the factor of either .40 or lower (1 cubic inch to 1 inch...0.5541125541126) to determine the amount of oils that a soap mold will hold.

Depends on how you set up the problem, but yes, you could use this conversion. I re-created the "0.40 rule calculations" a couple of years ago and figured out that someone decided to design a hypothetical soap recipe made with "full water" and a typical superfat. They calculated the volume of soap batter made with that recipe, and correlated this volume with the weight of the oils in the recipe. Factors involved are the density of water and the density of oil, and assumptions about superfat %, water content, and such.

Why would some people use 0.39 (or other number) rather than 0.40? Simple -- this rule is accurate only if the assumptions used to create this rule are followed. It will not be as accurate if the assumptions are not met. The 0.40 rule doesn't account for recipes made with more concentrated lye solution (aka a water discount). This means the level of soap in the mold will be lower if you use a "water discount" rather than "full water". The rule also doesn't account for any additives that add a lot of bulk to the soap -- salt, oatmeal, food purees, exfoliants, etc. A soap batter with bulky additives will fill the mold higher than expected.

Deanna also was talking about that. The 0.40 factor and the variations of it take in to account the average densities of things, the basic x cubic inches = y ounces and an average superfat thrown in.

It's not just about the 1 cubic inch to ounce conversion, as that assumes a certain density (usually water) and oils do not fit in to that. 1 litre of water is 1000g, but 1 litre of olive oil is less than 1000g.

It's not just about the 1 cubic inch to ounce conversion, as that assumes a certain density (usually water) and oils do not fit in to that. 1 litre of water is 1000g, but 1 litre of olive oil is less than 1000g.

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The 0.55 fl oz / 1 cu inch is just one part of the conversion. If you think about it ... 0.55 is not remotely close to 0.40 ... so that should be a clue that the 0.55 conversion isn't the whole story. The Gent is on target -- you can't just use that 0.55 conversion and get to where you want to go.

I'll be happy to write up the process of calculating that 0.40 number, if you or others are interested in the details. But I'm issuing a "geek alert" in advance on the explanation -- no whining that it's too much algebra.

And lye + water would also not be the same density of pure water.

ASSUMPTIONS

Assume a basic "full water" soap recipe. Choose a total oil weight of 10 ounces.

A "full water" recipe is based on 38% water as % of oils. If my oil weight is 10 oz, what is the weight of the water?

Water weight, oz = 10 oz oils X 38 / 100 = 3.8 oz (wt)

If using a balanced blend of fats, the lye concentration for a "full water" recipe is usually about 28%. So what is the weight of the NaOH needed?

Here is the algebra that must be solved to get this number:

(X, NaOH wt)/(3.8 oz water + X, NaOH wt) = 28 / 100

X = (0.28 X 3.8 ) / (1 - 0.28 )

The final answer:

X, NaOH weight = 1.48 oz

SUPPORTING INFO

Specific gravity of 28% lye solution is 1.310 (Dow Chemical Co.)

Specific gravity of a typical soaping fat is about 0.92 (various sources)

Conversion from fluid ounces to cubic inches: 1 cu in = 0.554 fl oz (from Spice)

CALCULATIONS

What is the volume of oils?

Weight of oils = 10 wt oz

Volume of oils = 10 wt oz / 0.92 = 10.87 fl oz

What is the volume of the 28% lye solution?

Weight of lye solution = 3.8 wt oz water + 1.48 wt oz NaOH = 5.28 wt oz

Volume of lye solution = 5.28 wt oz / 1.310 = 4.03 fl oz

What is the total volume of soap batter based on 10 ounces (wt) of oils?

Total volume of soap batter = Oil volume + Lye solution volume

Total volume of soap batter, fl oz = 10.87 fl oz + 4.03 fl oz = 14.90 fl oz

Total volume of soap batter, cu in = 14.90 fl oz / (0.554 fl oz/cu in) = 26.87 cu in

RESULTS

A basic "full water" soap recipe using 10 wt oz of oil will fill a mold that has a volume of 26.87 cu in.

That means for every 1 wt oz of oils used in a recipe, the soap batter needs 26.87 / 10 = 2.687 cu in of mold volume.

For any given weight of oil, what volume of mold is needed?

Mold volume, cu in = 2.687 X (Oil, wt oz)

For a given mold volume, what weight of oil is needed?

Oil, wt oz = (Mold volume, cu in) X (1/2.687)

The division problem of 1/2.687 = 0.37 so rewrite the previous equation so it looks more like the "0.40 rule" equation:

CONCLUSIONS

The factor I calculated is 0.37, not 0.40. This means if I had created this rule, I would call it "DeeAnna's 0.37 rule", not the "0.40 rule."

Why was a factor of 0.40 used in the original rule rather than 0.37?

One possibility is perhaps the original person who came up with the "0.40 rule" used slightly different assumptions than I did.

Or perhaps the original person wanted the mold to be a bit larger than needed so the soap batter did not fill the mold right up to the brim. The 0.40 factor increases the mold size a bit -- about 8% -- compared with using 0.37.

If you want some room for a sculptured top on the soap, to allow a lid to be put on the mold and not touch the soap, or just to allow for a bit of error, the 0.40 factor makes sense.

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The formula I use does not tell me how much batter I can put in the mould only how much oil. No matter which number I use I usually would need to make small adjustments to completely fill but no over flow the next time. Don't ask. I keep an oval bar set at the ready.

As I found out, the conversion factor for metric is 0.7, not 0.4. I had some very short slices of soap

This is incredible; I dont know where you live, but this makes want to meet you. Genius!The 0.40 rule -- how was it calculated?

ASSUMPTIONS

Assume a basic "full water" soap recipe. Choose a total oil weight of 10 ounces.

A "full water" recipe is based on 38% water as % of oils. If my oil weight is 10 oz, what is the weight of the water?

Water weight, oz = 10 oz oils X 38 / 100 = 3.8 oz (wt)

If using a balanced blend of fats, the lye concentration for a "full water" recipe is usually about 28%. So what is the weight of the NaOH needed?

Here is the algebra that must be solved to get this number:

(X, NaOH wt)/(3.8 oz water + X, NaOH wt) = 28 / 100

X = (0.28 X 3.8 ) / (1 - 0.28 )

The final answer:

X, NaOH weight = 1.48 oz

SUPPORTING INFO

Specific gravity of 28% lye solution is 1.310 (Dow Chemical Co.)

Specific gravity of a typical soaping fat is about 0.92 (various sources)

Conversion from fluid ounces to cubic inches: 1 cu in = 0.554 fl oz (from Spice)

CALCULATIONS

What is the volume of oils?

Weight of oils = 10 wt oz

Volume of oils = 10 wt oz / 0.92 = 10.87 fl oz

What is the volume of the 28% lye solution?

Weight of lye solution = 3.8 wt oz water + 1.48 wt oz NaOH = 5.28 wt oz

Volume of lye solution = 5.28 wt oz / 1.310 = 4.03 fl oz

What is the total volume of soap batter based on 10 ounces (wt) of oils?

Total volume of soap batter = Oil volume + Lye solution volume

Total volume of soap batter, fl oz = 10.87 fl oz + 4.03 fl oz = 14.90 fl oz

Total volume of soap batter, cu in = 14.90 fl oz / (0.554 fl oz/cu in) = 26.87 cu in

RESULTS

A basic "full water" soap recipe using 10 wt oz of oil will fill a mold that has a volume of 26.87 cu in.

That means for every 1 wt oz of oils used in a recipe, the soap batter needs 26.87 / 10 = 2.687 cu in of mold volume.

For any given weight of oil, what volume of mold is needed?

Mold volume, cu in = 2.687 X (Oil, wt oz)

For a given mold volume, what weight of oil is needed?

Oil, wt oz = (Mold volume, cu in) X (1/2.687)

The division problem of 1/2.687 = 0.37 so rewrite the previous equation so it looks more like the "0.40 rule" equation:

Oil, wt oz = 0.37 X (Mold volume, cu in)

CONCLUSIONS

The factor I calculated is 0.37, not 0.40. This means if I had created this rule, I would call it "DeeAnna's 0.37 rule", not the "0.40 rule."

Why was a factor of 0.40 used in the original rule rather than 0.37?

One possibility is perhaps the original person who came up with the "0.40 rule" used slightly different assumptions than I did.

Or perhaps the original person wanted the mold to be a bit larger than needed so the soap batter did not fill the mold right up to the brim. The 0.40 factor increases the mold size a bit -- about 8% -- compared with using 0.37.

If you want some room for a sculptured top on the soap, to allow a lid to be put on the mold and not touch the soap, or just to allow for a bit of error, the 0.40 factor makes sense.

Maybe the .4 was simply determined empirically. Make batter, fill mold, get weight, do arithmetic. That would be sensible because a purely theoretical calculation could be based on incorrect or oversimplified assumptions. One would probably not declare a rule without performing an experiment.The factor I calculated is 0.37, not 0.40. This means if I had created this rule, I would call it "DeeAnna's 0.37 rule", not the "0.40 rule."

Why was a factor of 0.40 used in the original rule rather than 0.37?

One possibility is perhaps the original person who came up with the "0.40 rule" used slightly different assumptions than I did.

My point in going through the math is that people repeatedly ask how this thing came to be, and Spice wondered about this at a moment when I had the time to answer in detail. It's good to help people better understand what they're doing by showing there really is some useful logic behind some of the odd "rules" of soaping.

Spice -- Glad I could help. I know math isn't your strong suit, so I hope I didn't overwhelm you. I hope you can get your soap recipes tweaked to fit your molds!

Patrick -- Bribes are always good to have on hand! I have been doing much the same thing as you do with my dribs and drabs -- in fact I'm thinking about increasing my batch size a bit so I have extra batter to make more of these handy little soaps -- and make them look a little nicer.

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