If you measure a tds of 1.4%, and you used a brew ratio of 15, what is the percent extraction?

Answer: the extraction is 18.2%.

Explanation:

Let's see few definitions:

TDS = Total Dissolved Solids = solids dissolved in the brew

PE = Percent Extraction = percent of solids extracted from the dry coffee grounds

The percent extraction can be calculated by the formula:

PE = TDS * Rm

where

Rm = ratio between the mass of the brew and the mass of dry grounds

Now, you need to consider the following facts:

1) every 1g of coffee absorbs 2g of water

2) the given brew ratio is 1:15, which means that for every 1g of grounds we use 15g of water

Let's call

x = grams of coffee grounds we want to use

Therefore the mass of the brew will be:

m (brew) = water we use - water absorbed by the coffee

= 15·x - 2·x

= 13·x

Therefore,

Rm = m (brew) / x

= 13·x / x

= 13

Hence, the percent of extraction will be:

PE = TDS * Rm

= 1.4 * 13

= 18.2