<p>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.</p>

<p>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 <code>15 - 4 = 11</code> which gives you the amount of water you need to add in whatever units you measured the amount of concentrate you started with.</p>

<p>Using your example numbers:</p>

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

<p>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 <code>25g x 15 = 375g</code> of water must be added.</p>

<p>The answers align.</p>

<p>In general:</p>

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

<p><em>Units</em> are any form of measure of the liquid mass being used, in g, mL or others.</p>

CC BY-SA 3.0
2017-01-11T12:47:52.197Z
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
CC BY-SA 3.0
2017-01-11T19:37:28.010Z
Thank you so much! I didn't believe you and I looked for equations involving  [dilution](https://en.wikipedia.org/wiki/Dilution_(equation)), 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
CC BY-SA 3.0
2017-01-12T09:48:31.887Z
You're welcome! I'm glad I could help :)
Shiri
CC BY-SA 3.0
2017-01-11T09:42:42.533Z
2017-01-11T09:50:20.040Z
2017-01-11T09:50:20.040Z
Shiri
<p>Using the dilution equation (assuming <strong>(incorrectly)</strong> that the moles concentration, correspond to the ratio of coffee:water of brewed product), the problem states:</p>

<pre><code>C1 = cold-brew initial ratio
C2 = cold-brew final ratio
V1 = volume of initial cold-brew to consider
V2 = desired final volume
</code></pre>

<p>The dilution equation states:</p>

<pre><code>C1*V1 = C2*V2
</code></pre>

<p>Replacing:</p>

<pre><code>(1/4)*100 = (1/15)*V2
V2 = (100*15)/4
V2 = 375 grs
</code></pre>

<p>But, to achieve this 375grs final, we must dilute the original solution, </p>

<pre><code>V2 - V1 = 375 - 100 = 275 grs of water.
</code></pre>

<p>Same result as <a href="https://coffee.stackexchange.com/users/1702/shiri">Shiri</a>. </p>

CC BY-SA 3.0
2017-01-11T19:47:38.037Z
2017-01-11T19:47:38.037Z
2017-04-13T12:51:53.733Z
Omar Miranda
<p>Imagine I produce a concentrated Cold-Brew, with a 1:4 ratio.</p>

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

<p>For the response consider explaining the math with:</p>

<ul>
<li>100grs of concentrated Cold-brew (brewed with 1:4 ratio)</li>
<li>Achieve a final beverage of 500grs (<strong>must have</strong> a 1:15)</li>
</ul>

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

CC BY-SA 3.0
2017-01-10T20:56:06.303Z
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
<cold-brew>
Calculate diluted concentration of cold-brew
Omar Miranda
# Calculate diluted concentration of cold-brew

(Asked by: username_0 on 2017-01-10)

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.

**Tags:** cold-brew

> **Comments:**
> **username_1**: 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.  

---

## 2 answers

### Answer by username_2 on 2017-01-11. Score: 2 | Accepted answer

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.

> **Comments:**
> **username_2**: 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.  
> **username_0**: Thank you so much! I didn't believe you and I looked for equations involving  [dilution](https://en.wikipedia.org/wiki/Dilution_(equation)), did the math and it actually corresponds to your results. Now that I backed up with science, I'm a bit more confident :)  
> **username_2**: You're welcome! I'm glad I could help :)  

---

### Answer by username_0 on 2017-01-11. Score: 0

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 username_2.


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