The extraction percent of coffee could be calculated with a Petri dish, stove and a precision scale, if you don't have access to a refractometer.
I assume, the original question here is: How does one calculate extraction percent? If this is the question, the answer is simply a refractometer as it directly reads the extraction percent.
However, the main problem is what could you do if you don't have a refractometer, or you are not assured with the quality of your refractometer. This boils down the subquestion: is it necessary to have a refractometer to calculate the TDS?
Actually, before the invention of refractometers (the device that checks the opacity of a liquid, so it could reason how many irregularities exists in it), chemists were able to calculate total dissolved solids in a solution by simple methods. I will explain one here. That, you can make at home without precision. And repeat at a lab environment with high precision.
- Find a very thin, light heat-resistant glass, preferably a Petri dish. Put it on (precision) scale and zero your scale.
- Put a fair amount of (say, 10 grams) brewed coffee in the Petri dish while it is on the scale.
- Place the Petri dish in the stove, set it to 100 °C. Wait until all water vaporizes and coffee remains dry out completely.
- Put the Petri dish on the scale again. You have weighted the total dissolved solids.
So, you now have all the required mass you need for your formulas.
- Be careful to be clean at all points. E.g. your sweat prints, etc. may affect the weight as the mass will be fairly small.
- Your accuracy increases while the weight of Petri dish decreases and the amount of brewed coffee used in this method increases.
- Use a scale as precise as possible.
- This methodology cannot weight the aromatic oils as everything vaporizes. However, by definition TDS does not include aromatic oils. So, I don't care about them that much.