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Thanks to generous donations on this site, we finally raised the $650 to have a nutritional analysis for aquafaba performed by Dr. Legg at RL Food Testing Laboratories. In short, if you're interested in calories, there's about 3-5 calories per US Tbsp of aquafaba, and the concentrations of everything else is so low as to not even register on a US FDA food label (see below).
This is the brand of aquafaba that was tested:
This brand is salt-free aquafaba from chickpeas and was passed through a super fine mesh before analysis to remove particulate matter. The aquafaba has no added salt, whips up into a foam with stiff peaks in just 1-2 minutes, and has the perfect consistency for all known applications.
Brands of aquafaba vary in their consitency, salt, and preservative content. Aquafaba made from soy or other legumes may be different. Also, if you're making it on your own, you won't know the exact concentration. You can use these results to get you in the ballpark, though.
Note: the label shows 5 calories per US Tbsp, but there are rounding conventions used in generating labels, especially when the nutritional information is closer to nothing. If you want to be more precise, you can see from the analysis, that there are about 32 calories per can of aquafaba, given one can of aquafaba is 180g or 3/4 cup. That's less than 3 calories per US Tbsp of AF.