# The Mathematics of Weight Loss

Most of us want to lose some weight, whether it’s 5 lbs. or 50+ lbs. Given the prominent desire to lose weight, why is it that we struggle with weight loss on a societal level? Why do some of us drop weight overnight, never to gain it back, while others struggle for years to lose even 2 lbs.? And why do others seem to yo-yo with their weight, dropping 15 lbs. in one month only to gain back 25 lbs.three months later? Given all the back and forth between the contributing to factors to our collective weight gain – carbohydrates, sugar, fat, processed foods, etc., it can be disheartening for anyone wanting to shed those pounds. But what if what we were taught about weight loss was completely wrong? What if the rules and principles that were taught to us as children and adults were based on flawed science and outdated research? As it turns out, that’s exactly what happened and it’s precisely why this article talks about the mathematics of weight loss.

The 1st Law of Thermodynamics

Before we get into the math, let’s first discuss the 1st law of thermodynamics. This law applies to human physiology and states that:

Energy is neither created nor destroyed but can transform into different forms.

This is represented by the equation below:

Es = E1 – E0

Es represents the rate of change in the body’s macronutrient stores. This value can be negative, positive, or zero. E1 primarily represents the chemical energy that is available from the food and beverages we consume. E0 represents any radiant, conductive, and convective heat loss, in addition to any work performed by the system (the human body), and the latent heat of evaporation.

Therefore, Es is the difference between the energy we consume and the energy our body uses. If throughout the day, you consume more calories than your body needs, then Es is positive. This means you gain weight. If you consume less calories than your body needs, then Es becomes negative and you hypothetically lose weight. And if Es is equal to E1 – E0, i.e. 0, then you maintain your weight. Sounds simple enough, right?

Although this sounds simple, the truth is it’s actually anything but. While E1 represents the energy obtained from carbohydrates, protein, and fat, E0 represents the rate at which the body expends energy. And this rate, i.e. your metabolism, actually varies from day to day across your entire lifespan. Growth, body maintenance needs, physical activity, pregnancy, and lactation are just a few factors that impact the body’s daily metabolic rate. Once this is taken into account, it quickly becomes clear that applying an equation to determine the appropriate daily caloric for any individual isn’t a clear cut science at all. Even in their 2012 statement, Energy Balance and its Components: Implications for Body Weight Regulation, the American Society for Nutrition stated:

“Although it is clear that E1 and E0 are part of a biologically regulated system, the exact nature of how this system works in humans has not been fully established.”

Unfortunately, this isn’t the only factor that plays into the mathematics of weight loss. Let’s move onto the first myth we’re debunking in the mathematics of weight loss which is the 4/4/9 rule.

The Myth of the 4/4/9 Rule

The 4/4/9 Rule is another factor that has contributed to the misinformation surrounding the mathematics of weight loss. This rule refers to the number of calories that can be found in 1 gram of carbohydrates, 1 gram of protein, and 1 gram of fat, respectively. There are 4 calories in 1 gram of carbohydrates, 4 calories in 1 gram of protein, and 9 calories in 1 gram of fat. Or at least that’s what they teach nutrition and health professionals who, in turn, teach this to clients, patients, and the general population at large.

The truth is that these numbers are population averages that represent the amount of energy available to cells for carrying out biological processes. Given that these are population averages, the numbers actually vary from individual to individual. In fact, the amount of available calories from any macronutrient are influenced by numerous factors including how the food is prepared, the individual’s gut microbiome, and their overall diet composition. Even how well the food is chewed can impact how many calories are actually available to the body’s cells.

Needless to say, there’s no way of truly knowing how many calories are contained within 1 gram of carbohydrates, protein, or fat. This ultimately means that the 4/4/9 rule is unreliable. Despite this, it remains the best tool that nutrition professionals have at their disposal in terms of calorie calculations.

The 3,500 Calorie Myth

As stated in the article, The Science of Weight Loss, the teaching that there’s 3,500 calories in 1 lb. of body fat is a myth. If this teaching were accurate, then creating a deficit of 500 calories per day should result in a net 1 lb. weight loss over the course of a week. However, this often doesn’t hold true over the long term. The reason this doesn’t hold true is because it assumes that weight loss is linear. But we now know it isn’t.

Weight Loss is NOT Linear

The human body requires different amounts of energy depending on its size. The Resting Energy Expenditure (REE) of the individual, that is the amount of calories required to maintain the body in a total state of rest, decreases as the mass of an individual decreases. To put it simply, think of a SUV versus a sedan. Which car requires more fuel? The SUV requires more fuel because it’s larger.

Therefore, as an individual loses weight and reduces their body mass, the amount of calories their body needs is also decreased. Therefore, weight loss is not linear. In order for weight loss to be linear, your body must always require the same amount of energy regardless of mass. But this isn’t how human metabolism works.

Fortunately, the 3,500 calories per pound of body fat myth was debunked years ago.

Don’t Lose Hope