Dosing Trader Joe’s cold brew coffee concentrate

The 32 fluid ounce cold brew concentrate at Trader Joe’s contains the equivalent of about 96 ounces of coffee beverages when reconstituted with water or milk according to their website. The bottle says that it makes 12 8-ounce cups of coffee.

The label does not tell you the caffeine content. We can assume that the Trader Joe’s product follow’s FDA guidelines when making their label. Per FDA guidance for industry, “caffeine content varies in different products” but “a typical eight-ounce cup of ground coffee contains approximately 95 milligrams of caffeine”.

If there is enough caffeine to make 12 8-ounce cups, then there is 1200 mg of caffeine in the cold brew container. That means, per fluid ounce of concentrate, we have $1200/32$ or 37.5 mg per fluid ounce. A standard cup’s worth of caffeine is 2.5 fluid ounces of concentrate or 74 ml.

What about caffeine per ounce? Ounces are a weight unit and fluid ounces are a volume measurement. We must multiply the fluid ounce value by the density (ounce per fluid ounce) to get the ounce value. The composition of cold brew is typically a 1:4 coffee to water ratio. The density of coffee grounds is about 0.32 g/cubic centimeter which is ~0.33 ounce/fl ounce. In a 1:4 ratio, the density of cold brew is $\frac{1 \cdot 0.33 + 4 \cdot 1}{(4 + 1)} = 0.87$ ounces per fluid ounce. So, there is $37.5 \cdot 0.87 = 32$ mg of caffeine per ounce. A standard cup’s worth of caffeine is 3 ounces of concentrate.