# How is the weight gain formula consistent with the law of conservation of mass?

Here are some points I have come to understand:

• Weight gain is a result of caloric surplus; specifically, every 3500 calories of surplus consumed corresponds to about 1 pound of additional bodyweight gained.
• One gram of fat contains about 9 calories.
• One pound is about 453.59 grams.

So, putting this all together:

A person who consumes 1 lb of pure fat as caloric surplus should expect to gain...

(453.59g) * (9 cal/g) / (3500cal/lb) = 1.17 lb of body mass.

Effectively, a person could gain more mass than they consume. Is this correct?

Where does this mass come from?

(I would guess that some of the mass might come from inhaling air, but I am under the impression that respiration is a source of losing mass, not gaining it. Happy to be shown otherwise!)

• "About" one pound, not "exactly" one pound, and it's wildly variable based on the person (e.g., for a high-level overview, see things like this article. Nov 17, 2021 at 21:47
• Have you accounted for poop? Nov 18, 2021 at 1:13
• 3500 calories = 1 lb is a misconception, actually. It's the result of trying to make a complex process simple, and relies on shaky math.
– JohnP
Nov 18, 2021 at 15:15

Firstly, it's worth noting that the 3,500 kcal/lb figure comes from a 1958 review paper, and only applies to weight loss on a high protein diet or weight gain that is not immediately following a period of caloric restriction (in which case replenishing glycogen stores could result in larger weight gains with only relatively small caloric surpluses).

This paper makes the following conclusions:

The low-calorie diets on which individuals are placed for the purpose of weight reduction should be high in protein so that protein and glycogen will be approximately in equilibrium. The calorie deficit will be made up chiefly by the catabolism of fat. Under the circumstances (high-protein intake) the caloric equivalent of one pound of body weight lost is approxmately 3,500 cal.

The caloric equivalent of one pound of body weight gained is dependent on the state of the protein and carbohydrate (glycogen) stores. If the protein and glycogen stores have been depleted as the result of fasting, their replenishment will be associated with a concomitant deposition of large quantities of water. During this period the caloric equivalent of one pound of body weight gained will be markedly less than 3,500.

When a state of protein and glycogen equilibrium is reached, all food ingested in excess of the amount necessary to maintain caloric equilibrium will be converted into fat (adipose tissue). The caloric equivalent of one pound of body weight gained will then be 3,500. In fasting there are always decided negative protein and carbohydrate (glycogen) balances. The catabolism of protein and glycogen is asso- ciated with losses of large quantities of water. The caloric equivalent of one pound of body weight lost in fasting (negative nitrogen balance) is always markedly less than 3,500.

Now, the question itself is problematic, because it is not possible to consume 1 lb of pure fat specifically as a caloric surplus. Let's say someone's maintenance level is 2000 kcal/day, and they normally eat that as about 100 g of protein, 250 g of carbohydrates, and 67 g of fats. Even if they add 1 lb (454 g) of fat intake to that, they're not eating an excess of 1 lb of fat, they're eating an excess of 4082 calories, and their overall intake throughout the day has been made up of 100 g of protein, 250 g of carbohydrates, 521 g of fat, and, let's say 2 litres of water. They don't get to decide which part of their food intake makes up the "excess", and in total, they're consuming almost 3 kg of food and water. So, crucially, they do have materials other than fat available.

You are correct that if the body were to store 1 lb of fat (~4082 kcal) with an energy intake requirement of only a 3500 kcal surplus, that would violate the laws of physics. However a bodyweight gain of 1 lb does not indicate that the body has stored 1 lb of fat. At most, the body could have stored 389 g (3500 kcal) of fat, and the remaining 65 grams or more of weight gained will come from increases in total body water due to the increased size of the body, and stored proteins and other cell components that are necessary to accomodate the increasing volume of fat being stored.

• Great, thank you for this. I realized the assumptions made were kind of crude, but they are extremely common and thrown around quite liberally in various fitness discussions. I think your last sentence in particular helps give a concrete answer to the issue.
– Zayn
Nov 19, 2021 at 14:44