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The Science of Coffee

In order to brew coffee precisely, you will need to be able to accurately measure at least one of volume or mass. Water has a well-characterized density as a function of temperature, and can be measured by volume or mass with equal accuracy. Coffee beans are more variable, both because their density differs and changes considerably as they are roasted, and because they pack imperfectly; they are thus better measured by mass if possible.

SubstanceMetricImperial
Room Temp Water (20 C)0.9982 g/ml1.041 oz/floz
Boiling Water (100 C)0.9584 g/ml1.000 oz/floz
Green Coffee (whole)0.73 g/ml0.76 oz/floz
Light Coffee (whole)0.50 g/ml0.51 oz/floz
Dark Coffee (whole)0.33 g/ml0.34 oz/floz

Another factor to take into account is that not all of the water which goes in ultimately comes out. Coffee grounds retain between 1.8 and 2 times their own mass in water. Also, many coffee machines lose some water as vapor and remaining unused in the reservoir; this differs from one machine to the next, and you may want to measure your own. If we assume 20% extraction of the coffee mass, 2x the coffee weight in retained water in the grounds, and no other losses, we can calculate the desired ratio of coffee to water:

Desired ConcentrationCoffee to Water, by mass
0.012 (1.2%)0.0536
0.013 (1.3%)0.0575
0.014 (1.4%)0.0614
0.015 (1.5%)0.0652
0.016 (1.6%)0.0690

If you don't have a scale, it gets more difficult. The easiest thing to do is just buy a scale - you can get a perfectly adequate one which will go up to a few hundred grams or so for less than $20. Failing that, it is possible to measure coffee by volume, but several corrections are necessary. Firstly, you must know the density of your coffee. Since most coffee is sold by weight, the way to ascertain this is to take the full package of coffee before any is used and measure its volume in measuring cups. Then calculate the density of the coffee in grams/ml or oz/tablespoon or other convenient units. Then, you must calculate a correction factor for the scoop you are going to use - even if it is of known volume, coffee beans are large with respect to a one-tablespoon scoop, and will pack differently depending on the shape of the scoop. In my tests, I found that a conical tablespoon scoop held only 0.78 tablespoons of coffee, and a hemispherical one held 0.92. You can calibrate yours by filling it repeatedly with coffee and emptying it into a larger measuring cup until full - in the larger cup, the bean packing issue is less significant. If you worked with ground coffee instead of whole beans, it would simplify the measuring scoop issues, but would be problematic to get the initial density measurement.