# Calculate diluted concentration of cold-brew

Imagine I produce a concentrated Cold-Brew, with a 1:4 ratio.

How can I make a cup of diluted cold-brew that contains the standard ratio (1:15) ?

For the response consider explaining the math with:

• 100grs of concentrated Cold-brew (brewed with 1:4 ratio)
• Achieve a final beverage of 500grs (must have a 1:15)

PS: I don't think that is as simple as adding the n remaining parts, that's the reason why I'm asking this.

• I recommend you to change the given example to 100 gr (ml) concentrate and 375 gr (ml) regular. Then, you can start with 25 grams of coffee for each. – MTSan Jan 10 '17 at 20:56

## 2 Answers

The math is fairly simple. You know for how much concentrated cold brew you will be using that it is at a ratio of 1:4. Since the resulting concentration of the cold brew is constant (since it has already been brewed) we only really care about the parts of water that are in it; 4 parts.

Therefore to calculate how much water you need to add to dilute your 1:4 concentrate into a 1:15 cup, divide the amount of concentrate you are using by 4 and then multiply that by the remaining parts you wish to add, which is `15 - 4 = 11` which gives you the amount of water you need to add in whatever units you measured the amount of concentrate you started with.

Using your example numbers:

Start with 100g of cold brew concentrate at 1:4 ratio. Each part of water is therefore `100/4 = 25g`. The amount of water you will need to add is therefore `11 x 25g = 275g` to result in a total amount of 375g in your final cup.

Check the final answer by doing a reverse calculation. If the concentrate is 1:4 and you have 100g of it, it means you started with 25g of ground coffee. Therefore making a 1:15 ratio cup of coffee with 25g of coffee means `25g x 15 = 375g` of water must be added.

The answers align.

In general:

For an amount of cold brew to be diluted, `c` units, which has a coffee-to-water ratio of `1:n`, the amount of each part of water in the cold brew, `w` equals `c/n`. The amount of water to be added to achieve a final ratio of `1:m` is therefore `w x (m-n)` units.

Units are any form of measure of the liquid mass being used, in g, mL or others.

• To address your second point of achieving 500g of diluted coffee at 1:15 ratio using 100g of concentrate at 1:4; it is simply impossible. If you are given 100g of concentrate at 1:4 as a constant, the result of a ratio of 1:15 is achieved by adding a specific amount of water. If you want to achieve 500g in your resulting cup, the final ratio will not be 1:15 if you started with 100g of 1:4. – Shiri Jan 11 '17 at 12:47
• Thank you so much! I didn't believe you and I looked for equations involving dilution, did the math and it actually corresponds to your results. Now that I backed up with science, I'm a bit more confident :) – Omar Miranda Jan 11 '17 at 19:37
• You're welcome! I'm glad I could help :) – Shiri Jan 12 '17 at 9:48

Using the dilution equation (assuming (incorrectly) that the moles concentration, correspond to the ratio of coffee:water of brewed product), the problem states:

``````C1 = cold-brew initial ratio
C2 = cold-brew final ratio
V1 = volume of initial cold-brew to consider
V2 = desired final volume
``````

The dilution equation states:

``````C1*V1 = C2*V2
``````

Replacing:

``````(1/4)*100 = (1/15)*V2
V2 = (100*15)/4
V2 = 375 grs
``````

But, to achieve this 375grs final, we must dilute the original solution,

``````V2 - V1 = 375 - 100 = 275 grs of water.
``````

Same result as Shiri.