Confused about calorie math

1 lb of body fat is not 100% fat, the same as 1 lb of muscle is not 100% protein.

Hoping Google can stop me from looking for the research again...

http://www.myfitnesspal.com/topics/show/816892-drop-10-pounds-in-30-days-the-math-behind-it

Adipose tissue is not 100% fat. To quote http://www.sportsci.org/encyc/adipose/adipose.html :

"Approximately 60 to 85% of the weight of white adipose tissue is lipid, with 90-99% being triglyceride. Small amounts of free fatty acids, diglyceride, cholesterol, phospholipid and minute quantities of cholesterol ester and monoglyceride are also present. In this lipid mixture, six fatty acids make up approximately 90% of the total, and these are myristic, plamitic, palmitoleic, stearic, oleic, and linoleic. Varying the composition of your diet can vary the fatty acid profile in adipose tissue. The remaining weight of white adipose tissue is composed of water (5 to 30%) and protein (2 to 3%)."

Human muscle is about 16-21% protein.

Since the variability between people (and cells within the same person) make it impossible to determine the exact caloric value without dissection (and in the case of muscle, even the dissection method uses estimates since separating fat from within muscle fibre is too difficult), and the math to do it is too complex for me, I trust the averages of 3,500 kilocalories per pound of fat and 600 kilocalories per pound of muscle.

ETA: That is for losses and gaining fat, I'm not sure what the averages are for regaining muscle and gaining muscle. 2,500 kilocalories seems to be touted for bulking, but I think that is the "pound of muscle plus some fat gain that you'll later lose when cutting" figure.

Approximately 3,500 kcal per pound, so 3,500 / 0.454 = approximately 7,709.25 kilocalories per kilogram of body fat. There are 454 grams in a pound, so you don't really need a source saying how many calories are in a kilogram of body fat because we know how to convert between weighing systems.

Whether you go with 7700, 7710, 7709.25, or 7709.2511013215859030837004405286 kcal per kg, it probably doesn't matter because 3,500 kcal per lb is an approximation itself... 7,700 is a nice round number. To my knowledge, the exact number would be impossible to determine because even if there was a sci-fi scanner that could determine the makeup of all your cells you have no idea which cells would make up the next kilogram you lose.

Back home (long time ago), my dietitian also taught me 9k cal/kg so the "common wisdom" might be a cultural thing. She probably simply didn't know any better.

Seeing the number 9, it is feasible they meant/said/recalled 9 kilocalories per gram of fat. Can't be sure though.

If going with metric, I suppose the one thing to bear in mind is that a seventh of 7,700 is 1,100, so the metric goals on MFP are slightly more than the imperial goals (e.g. 0.5 kg/week ~= 550 kcal/day deficit, 1 lb/week ~= 500 kcal/day deficit).

ETA: It might also be entirely possible the experts don't know how to convert between metric and imperial, or that they don't know white adipose tissue isn't 100% fat. 9,000 calories should equal ~4.086 pounds of body fat, or ~1.855044 kilograms of body fat.

ETA2: Using the estimate of 9 kilocalories per gram of fat, losing 1 pound of body fat could (using the approximate numbers I quoted myself quoting) require a deficit of:

9*454*0.6*0.9 + 4*454*0.02 = 2,206.44 + 36.32 = 2,242.76 calories on the low end.
9*454*0.85*0.99 + 4*454*0.03 = 3,438.369 + 54.48 = 3,492.849 calories on the high end.

So a kilogram of body fat could require a deficit between 4,940 calories and 7693.5 calories, depending on the make-up of the cells utilised.

I have no idea if this is how the 3,500 and 7,700 numbers were reached though. It could be I have missed a multiplier (efficiency of lipolysis?)