1lb does not equal 3,500 calories
One of the most commonly held diet myths is "To lose one pound of fat you need to create a deficit of 3,500 calories". This is wrong at every level. First of all, one pound does not equal 3,500 calories, as we will show below. You will see this formula in government literature, in just about every diet book, in private health booklets and all over the internet. The next time you see it, or hear it, ask where it comes from. You will not get an answer. (I asked the following seven UK organisations: the National Health Service (NHS); the National Institute for Clinical Excellence (NICE); the Department of Health; the National Obesity Forum; the Association for the Study of Obesity; the British Dietetic Association and Dieticians in Obesity Management and five of these have no idea where it even comes from. The two that tried to prove it failed by a factor of about ten.) (I’ve since put this up as a full blog post).
The first part of the calorie formula is the assertion that one pound of fat contains 3,500 calories. You will struggle to find anyone who can demonstrate the precise calculation behind this, so I'll offer this as a suggestion:
1) One pound equals 454 grams (decimal places aside, this is a fact);
2) Fat has nine calories per gram (this is the universally accepted conversion, but it is an estimate and significantly rounded down from even the original estimate);
3) Human fat tissue is approximately 87% lipid (this is a widely accepted conversion, but it is also an estimate).
Putting these together, we can derive the sum that 454 grams of body fat tissue has approximately the calorific energy of 395 grams of pure fat (454 grams x 87%), that is 3,555 calories (395 grams x 9).
3,555 is close enough to 3,500 you may think, until you see the absurdity of how precisely the formula is applied. The National Obesity Forum web site states "one less (sic) 50 calorie plain biscuit per day could help you lose 5lbs (2.3kg) in a year - and one extra biscuit means you could gain that in a year!" (Ref 1) No it won't. I can't even get an estimate of the formula to closer than 55 calories 'out'.
With little effort I can find evidence in obesity journals that fat has anywhere between 8.7 (Ref 2) and 9.5 (Ref 3) calories per gram. The same obesity journal that says that human fat tissue can be 87% lipid also says that it may be 72% lipid (Ref 4).
Taking the extremes of these, we can establish a range whereby one pound of fat could contain anywhere between 2,843 and 3,752 calories. Given that it is currently held that one pound is 3,500 calories we could (according to this formula) inadvertently gain six stone every year at the low end of the calculation and lose almost two stone in the same year if one pound is 3,752 calories. The 3,750 calories is the assumption held in this classic article (Ref 3). Don't worry about any of this - because the formula doesn't hold at any other level either. (Please see footnote for calculation).
Ref 1: http://nationalobesityforum.org.uk/families/before-you-start-mainmenu-110/34-how-weight-loss-works.html.
Ref 2: Dr. Geoffrey Livesey, “The Calorie Delusion: Why food labels are wrong”, New Scientist, (15 July 2009). FAO Food & Nutrition paper 77: “Food energy - methods of analysis and conversion factors”, Report of a Technical Workshop, Rome, (December 2002).
Ref 3: Max Wishnofsky, "Caloric equivalents of gained or lost weight", The American Journal of Clinical Nutrition, (1958).
Ref 4: Bozenraad, Deutsche Archives Internal Medicine, (1911).
This calculation is done as follows: It assumes that a person can maintain weight at a daily intake of the calories assumed to equal one pound of fat. If we think one pound equals 3,500 calories and in fact one pound equals 2,843 calories, over a year, 657 ‘extra’ calories a day, simply from the formula ‘being wrong’, would add up to 239,805 extra calories and this, divided by 2,843 gives 84 pounds, or six stone. Adjust the calculations for women more typically maintaining at 2,000 calories a day and men more typically at 2,600 calories a day and the inaccuracy of the formula still creates wide disparity.