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I have recently read on this Q & A site that the rule of thumb that 37 000kJ is required to burn 1kg of fat is incorrect. I have been down-voted by some for quoting this figure.

Is it true that the above relationship is a rough estimate of fat loss, or has it been shown to be untrue. I'm interested in seeing any studies you can give that indicate your point of view.

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One issue with "X calories deficit = Y lbs of weight loss" is that it requires knowing your daily calorie burn, but that figure will start changing as soon as you start losing weight, or changing your diet and activities. – Kate Jan 25 at 2:43
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The comments on this answer are pretty close to what you want, Chris. There's also significant discussion in this question. – Dave Liepmann Jan 25 at 6:28
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@michael generally has something to say on this topic; maybe he could chime in with a definitive answer. These comments and this chat may be of relevance, the latter containing a link to a study as well as some criticism of that study. – Dave Liepmann Jan 25 at 6:42
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Agreed. It was discussions with @michael that led me to dig further into the current research, and I've found that while caloric deficit (more than diet) is the biggest factor in weight loss, it's not a straight 3500 cals = 1 lb of fat loss. It is still a mantra repeated in most textbooks, but it's much more complicated than that. – JohnP Jan 25 at 14:33
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@JohnP That's awesome. I think that this question is really begging for multiple semi-competing comprehensive answers that talk about those complexities of where the 3500 calories idea breaks down. Unfortunately I'm not knowledgeable enough on that side of things. – Dave Liepmann Jan 25 at 17:56
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The 37,000 number is correct, but it can be misleading in a couple of ways.

A kg of fat contains 7700 calories of food energy, so to lose that 1kg of fat, you need to burn 7700 more calories than you take in. This is well-understood and agreed upon.

When you start talking about kJ, it gets a bit more complicated and confusing. Kj is a measure of the amount of work done - for example, I have a power meter on my bicycle, and it can measure the amount of work that is done in kj. Let's assume I go out on my bicycle and do 1000 kj of work. Now, a calorie is roughly 4 times bigger than a kj (see note 1), so that would imply that I only used about 250 calories of food energy. However, humans around 20-25% efficient in converting food energy to mechanical energy, which means it takes 250 / 25% = 1000 calories of food energy to do 250 calories of mechanical work. So... what everybody does is just consider them to be equivalent.

Unless you have a way of determining power expenditure, it makes a lot more sense to just deal with calories instead of kj.

note 1: When we talk about calories WRT food, we are really talking about kilocalories in the physics sense, but nobody calls them that.

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Actually, the logic you applied to kJ applies to kcal too! You cant exactly know how much nutrients is lost in the digestive proces of a particular person, and you dont know how effectively is he or she using the calories. The physics definition of calories is the amount of energy you need to warm 1g of water by 1K. The 4kcal/gram for carbs rules are such an approximation, that when combined with all the approximations of the daily energy expenditure, you cant really tell how much exactly youre taking in and expending. Thats why 3500kcal - 1lbs does not work. – K.L. Jan 31 at 11:42

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