There is a lot of scientific work done with regards to the reduction in caloric intake required to achieve a particular weight loss goal. The mathematics behind the science of weight loss are, in fact, quite fascinating and in this article, we will go over them in some detail. In doing so, we will address a common myth: that reducing your caloric intake by 3500 kCal for a week will result in a weight reduction of about 1 pound (0.454 kg) over that week.

The latter is a very pervasive myth with regard to the mathematics of weight loss. It has been propagated by many fitness, well-being and weight loss websites including the likes of Harvard Medical School, Mayo Clinic and the U.S. Surgeon General. Debunking this myth can help people get a better grasp on what it takes to lose weight.

The 3500 kCal per Pound of Weight Loss Myth The claim that in order to lose one pound of body weight per week you need to reduce your caloric intake by 3500 Calories per week (500 kCal per day) is a very pervasive myth which can be traced back to a 1958 paper. In that early paper on the mathematics of weight loss, human adipose tissue, where fat is stored, was calculated to contain the energy equivalent of 3500 kiloCalories. This led to the conclusion that you must reduce your weekly food intake by the equivalent of 3500 Calories.

However, this “rule” was questioned by a lot of research performed later on. As K.D.Hall puts it in his 2007 paper : “One of the most pervasive weight loss rules states that a cumulative energy deficit of 3500 kcal is required to lose 1 pound of body weight” Hall further elaborates on the widespread misuse of the so-called rule in a paper from 2011: This ubiquitous weight-loss rule […] was derived by estimation of the energy content of weight lost but it ignores dynamic physiological adaptations to altered body weight that lead to changes of both the resting metabolic rate as well as the energy cost of physical activity.

Unfortunately, this static weight-loss rule continues to be used for weight-loss counselling and has been misapplied at the population level to predict the effect of policy interventions on obesity prevalence.

Weight loss diet calories

Understanding why the 3500 Calorie rule for losing weight is a myth isn’t that difficult even to the uninitiated as long as they have expressed some interested in the mathematics of losing weight. The basic idea of weight loss science is to induce an imbalance between the energy you receive from food and the energy you expend in your daily activities.

To visualize this from a math perspective, if I is energy intake and E is energy expenditure, we want I to be less than E on a daily basis: I < E, which would, by the law of energy balance, lead to a reduction in weight as the body compensates the difference E – I by using up energy stored in different body tissues.

However, according to mathematics of weight loss proper, when you reduce your energy intake your body does not compensate for the difference by using only stored fat, which is an assumption behind the 3500-kCal rule. Your body also “burns” proteins and carbohydrates from body tissues which compose fat-free mass (FFM or LBM, lean body mass) such as the short-term glycogen stores, muscle, and others. The proportion of fat to fat-free mass lost during a calorie restricted diet varies depending on their initial ratio. Since the initial ratio changes dynamically, week over week, the proportion and thus the calorie deficit required changes as well.

Due to the vastly different energy densities of pure fat (9500 kCal/kg or 4313 kCal/lbs) and fat free mass (1000 kCal/kg or 454 kCal/lbs.) any change in the proportion can have a significant effect on the actual reduction in body weight since getting 2000 kCal from fat-free mass will reduce your weight by about 2 kg (4.4 lbs.) while doing the same from fat mass will only reduce it by 0.21 kg (0.46 lbs.).

This simple math proves quite eye-opening. Other factors influence the weight loss calculations in a dynamic way as well. For example, reducing the food intake also reduces the thermic effect of food (TEF, a.k.a. dietary induced thermogenesis or DIT). As result, you expend less energy to process and store energy from food which feeds back into the weight loss calculation and lowers the expected weight reduction.

Corrected Weight Loss Rule? Simple attempts to “fix” the 3500 kCal per lbs of lost weight rule might attempt to propose a higher or lower numerical value. However, such attempts are doomed to fail by way of simple mathematics since a lower value for the energy content of lost tissue will still not account for the dynamics of losing weight.

Nevertheless, note that the original rule of thumb does work in certain cases:

Another way to look at the 3500 rule

Anyone who’s been on a diet or attempted to lose weight in the past 30 years, a familiar piece of advice went something like this: “A pound of fat contains about 3500 calories. Simply subtract 500 calories per day from what you’re eating, which will create a deficit of 3500 calories over one week (500 calories/day x 7 days = 3500 calories). You’ll lose a pound each week and lose 52 pounds in one year!” It sounds really simple. And the math is right, a pound of fat contains about 3500 calories. But there are several reasons why this line of thinking is misleading.

The first thing to consider is that metabolism changes as weight loss occurs. Consider this example: a 40 year-old, mostly sedentary, 250 pound, 5’8” male needs around 2400 calories per day to maintain that weight (on average). His goal is to get back to around 190 pounds, where he was at before he became sedentary and started eating poorly. Let’s say this individual starts eating around 1900 calories per day. He should, theoretically, lose around a pound a week for a while. But let’s say he’s lost 40 pounds, putting him around 210 pounds. His body now needs around 2100 calories per day to maintain his new weight.

If he’s still following the same plan, he will no longer be losing a full pound every week. At this point, many people become frustrated and either give up on the changes they’ve made or totally change their approach. What they don’t realize is that they may still be moving towards their goals, simply at a slower rate than they initially did.

That’s okay.

Slight adjustments can be made, but patience is important in achieving and sustaining weight loss. Sometimes plateaus are even a part of the process. The wrong thing to do in this scenario is to continue progressively cutting calories until you reach a restrictive level (let’s say 1400 calories in the above scenario). By doing so, inevitably you will reach a point where your body, in a deprived state, starts pulling energy from muscle tissue and drastically slowing metabolism. This is a recipe for eventual weight re-gain and sets the individual up for weight cycling, which isn’t good news for your health.

Gradual weight loss is okay, and allows you to utilize lifestyle changes that you can keep at the end of the process rather than asking yourself “I can’t starve myself anymore…now what?” The National Institute of Health has developed a more realistic simulator for weight loss that accounts for metabolism changes, and gives you feedback if you set goals that are unrealistic in a certain time frame. It’s not a perfect model, but that doesn’t exist. Follow this link to see the NIH “Body Weight Planner.”

Some other problems with the 3500 calorie rule of weight loss include:

• Inaccurate calorie counting. We have more nutrition information available than ever, but it’s still very difficult to accurately estimate portions and calorie counts. In most studies, people consistently underestimate their calorie intake. This is compounded when we account for calories burned during exercise, which can also be difficult to accurately determine.

• The starting point is wrong. If an individual has been gaining weight and cuts 500 calories per day, that may only mean that they will now maintain their weight or gain weight more slowly than they have been.

• Not everyone wants to (or should) count calories. There are other strategies to lose weight outside of counting calories every day. In fact, many people do better on plans that do not involve calorie counting, which can be time-consuming, confusing, and can feed into anxiety and perfectionism around food which are detrimental and unnecessary.