Ask the Alchemist #168


Level: Novice

Reading time: 5-15 min (depending on how you follow maths)

I have a batch of 75% chocolate running.  70% cocoa nibs, 5% cocoa butter, the rest sugar.  I want to make it 80% by adding cocoa butter.  I started with 85 oz of nibs.  Can I just add the same amount of cocoa butter again?

Sadly, no you can’t.  But let’s run through the maths if you were to add that amount of cocoa butter and then how much you actually need to add.

It goes like this.

First I need to find out how much total chocolate you have so I can know how much cocoa butter you added.

T /  85 =  0.7  Rearrange that to:

T = 85 / 0.7 = 121.43 oz total chocolate

With that, I can get how much sugar.

121.43 * 0.25 = 30.36 oz sugar.

So you have

85 + 30.36 + 6.07 = 121.43 oz

If you add 6.07 oz more cocoa butter it is now

85 + 30.36 + 6.07+ 6.07 = 127.5 oz total chocolate

To find the new cocoa butter percent  it is

(6.07+6.07) / 127.5 = 9.52%

The new chocolate total percent is:

(85 + 6.07 + 6.07) / 127.5 = 76.2%

Not 80%, even though the cocoa butter is near 10% as the new total is higher.  The cocoa nib portion has dropped from 70% to 66.6%.

85 / 127.5 = 0.666 = 66.6 %

If you want to actually make it 80% you have to pull out algebra again.

0.8 = (85+6.07+x) / (121.43+x)

0.8 (121.43 + x) = 85 + 6.07 + x

97.144 + 0.8x = 91.07 + x

97.144 - 91.07 = x - 0.8x

6.074 = 0.2x

x = 30.37 oz

So, you make it all the way to an 80% bar with only adding cocoa butter you have to add a whopping 30.37 oz as:

(85 + 6.07 + 30.37) / (121.43 + 30.37) =0.8 = 80%

You didn’t ask,  but I would add more cocoa nibs and/or a mixture of cocoa butter.  Just for fun, let’s run through the maths involved in making it 75% cocoa nibs, 5% cocoa butter still, and sugar from your existing batch.

I’m going to take this in another direction calculation wise since we know how much sugar we have and don’t have to change it.

S = 30.6

We have decided it will be 20%, so we can get the new total from this:

30.6 / T = 0.2

T = 30.6 / 0.2 = 153

With that in hand, we can find out how much cocoa nib we need.

153 * 0.75 = 114.75

And since we had 85 oz:

114.75 – 85 = 27.75 oz cocoa nibs

We can do the same thing with the cocoa butter:

153 * 0.05 = 7.65

7.65 – 6.07 = 1.58 oz cocoa butter.

The main downside to this option is you have to refine your chocolate further.

Either way, there is the maths.  I hope that helps.

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