The Energy Balance Equation

by Fabio Comana, MA, MS on Feb 15, 2012

To battle obesity, we must understand the mathematics of weight loss and learn to look beyond the numbers.

We are taught that weight loss is simply an equation of calories in versus calories out. If only it were that simple.

There is no magic formula for weight loss, of course, but researchers have developed many mathematical models to help us better understand how the body sheds weight. This article examines major concerns associated with these calculations (they are far from perfect) and then discusses simpler solutions that empower all of us to confront one of the most vexing issues of our times.

That issue is obesity, and the facts are disturbing: Between 1995 and 2010, obesity in the United States increased at a staggering rate. In 1995, no state reported obesity levels above 20%. By 2010, no state reported obesity levels below 20% (CDC 2010). Coincidently, between 2000 and 2009 we have also witnessed an increase in the number of Americans meeting the minimal requirements for physical activity (CDC 2010). So why are obesity levels rising?

One key indicator is the American College of Sports Medicine’s recommendation of 2,000 kilocalories (kcal) of exercise per week for successful weight loss, compared with the minimal requirements targeting 1,000 kcal per week to improve health. People join health clubs to lose weight with the 1,000 kcal number on their minds, often not realizing that the 2,000 number represents how hard they must work to take off pounds.

Table 1 illustrates this point, comparing energy expenditure from 1 week of exercise against weekly caloric intake.

Table 1. Average Caloric Intake and Output for Men and Women, and Physical Activity as Percent of Caloric Intake

It appears many exercisers—especially beginners—will not burn enough exercise calories to lose weight unless they participate in longer, harder and more frequent bouts of physical activity. However, we must ask: Is 2,000 kcal a week realistic for new exercisers, given that higher volumes and intensities can discourage newcomers from sticking with a fitness regimen?

And there are many more complexities for newcomers to fitness. One of the most important fitness statistics is the body’s resting metabolic rate (RMR). RMR is the largest contributor to total daily energy expenditure (TDEE), and boosting RMR is a logical weight loss objective. For example, we might try building muscle mass to increase RMR by approximately 7%–8% or raising excess postexercise energy consumption (EPOC). But here’s the rub for fighting obesity: muscle mass will not demonstrate any significant increases for at least 1–2 months, and EPOC is neither large nor relevant for new exercisers.

We must also consider another compounding factor associated with exercise and weight loss: how moderate-intensity exercise may boost caloric intake by up to 383 kcal a day (Whybrow et al. 2008). Whether that increase is attributed to an exerciser’s need to satisfy hunger and replenish energy reserves or to the need to rationalize a reward for working out, these extra calories may impede weight loss.

While appetite needs to be controlled, denying hunger is a mistake. Failure to eat when hungry can suppress RMR by up to 20%, preventing weight loss (Hill 2004; Thompson, Manore & Thomas 1996). The impact can be significant when you consider that RMR generally accounts for 60%–75% of TDEE. For example, for an individual expending 2,000 kcal daily, a 20% reduction in RMR translates to 240–300 kcal daily—or 25–31 pounds over a year.

As we can see from this abundance of stats, mathematical calculation is at the very core of traditional weight management philosophy. While we must use a multipronged approach addressing both the physiological, psychological and emotional components of obesity and the social, cultural and environmental influences, there is almost no escaping the numbers.

Digging Into the Formulas

The foundation of weight loss formulas is total daily energy expenditure. There are numerous quick, gross ways to estimate TDEE, but several more-reliable methods dig deeper by including the critical RMR in their scientific formulas. Examples of these formulas include Mifflin-St. Jeor, Harris-Benedict, Owen, Katch-McArdle and Institutes of Medicine equations. The formulas may seem daunting at first, but familiarizing yourself with them now will help you appreciate the simpler approaches recommended later in this article.

First, we must respect the limitations of these formulas: while generally considered valid, they exhibit potentially large errors with obese and nonobese individuals, as illustrated in Table 2.

Table 2. Accuracy and Inaccuracy of Harris-Benedict and Mifflin-St. Jeor Formulas

The Harris-Benedict equation, created in 1919 and long considered the gold standard, is accurate up to 81% of the time in nonobese individuals, but it can also overestimate by 42%. The Mifflin-St. Jeor equation, created in 1990, has smaller margins of error and is considered the most accurate mathematical formula for the U.S. population (Weijs 2008). A major limitation with most of these formulas, however, is that they fail to consider the relative amounts of lean and fat mass, which significantly influence RMR. The Katch-McArdle formula, meanwhile, uses lean body mass; this improves the accuracy of this equation, but it still depends on a correct assessment of body fat percentage.

Crunching the Numbers

An individual’s energy output consists of several components:


To refresh your memory:

  • TDEE is total daily energy expenditure.

  • RMR is resting metabolic rate—calories expended while resting. RMR is generally 60%–75% of TDEE.

  • TEF is the thermic effect of food—the cost to chew, swallow, digest, absorb and store food. It generally represents 10% of TDEE.

  • TEPA is the thermic effect of physical activity—exercise, physical activity and nonexercise activity thermogenesis (NEAT), the energy of fidgeting or moving. TEPA generally represents 15%–30% of TDEE.

Calculating TDEE

Each formula in Table 3 uses two steps to determine TDEE:

1. Calculate RMR.

2. Multiply RMR by the activity factor score, which accounts for TEF and TEPA.

Table 3. Mathematical Calculations for Resting Metabolic Rate

As an example, we can use these equations to calculate TDEE for a relatively inactive 35-year-old female who stands 5 feet 5 inches (165 centimeters) tall and weighs 155 pounds (70 kg). She works as a software engineer, a predominantly seated occupation, and participates in about 30 minutes of light- to moderate-intensity activity two to three times a week.

Step 1: Calculating RMR

Harris-Benedict Equation

RMR = 447.593 + (9.247 × kg) + (3.098 × cm) – (4.33 × age)

RMR = 447.593 + (651.45) + (511.17) – (151.55)

RMR = 1,459 kcal

Mifflin-St. Jeor Equation

RMR = (9.99 × kg) + (6.25 × cm) – (4.92 × age) – 161

RMR = 703.79 + 1,031.25 – 172.2 – 161

RMR = 1,402 kcal

Step 2: Calculating the Activity Factor Score

This step determines the additional calories used through physical activity (TEPA) and food digestion (TEF). Those calories are calculated either by using a standard activity factor (SAF) or via a weighted activity factor (WAF) derived from a client’s activity logs. SAF scores are designated by selecting a predetermined level of activity that best represents the client’s activity throughout the day.

Harris-Benedict Standard Activity Factor Scores

Alas, SAF scores assume the accuracy of self-reported activity, and they have two more key limitations:

1. SAF does not consider activities outside of exercise. Exercise alone accounts for only a small portion of the total calories needed to balance an individual’s weekly caloric intake.

Consider that a week has 168 hours, of which we might spend 56–64 hours sleeping (energy cost = ~4,100–4,700 kcal per week for the average adult) and 3–5 hours exercising (energy cost = ~1,500–3,000 kcal). This total of ~5,600–7,700 kcal is a small fraction of the 17,528 kcal or 12,397 kcal consumed weekly by men and women respectively.

To avoid weight gain, we have to account for the remaining 99–109 waking hours, especially NEAT. The standard activity factors presented here do not account for NEAT, so the potential for error increases.

For example, consider the TDEE for someone who participates in moderate-to-intense exercise three to five times per week, but spends 10 hours a day seated, versus someone who manages only two to three bouts a week of light-intensity exercise, but works as a food server, constantly moving and carrying items for 6–8 hours a day, 5–6 days per week. SAFs would classify the light exerciser in a lower-activity category, but in reality he or she may be more active than the person who exercises more.

2. SAF does not examine exercise details. For example, a 60-minute, moderate-intensity circuit-training bout with 60-second recovery intervals between stations burns significantly fewer calories than a 60-minute moderate-intensity, steady-state cardio bout.

The Alternative: Calculating WAF

The recommended alternative is to calculate a weighted average factor (WAF) from an individual’s activity logs. Traditionally, for this purpose people maintain 24-hour activity logs for a minimum of 3 days, and a value is assigned to each activity (Table 4 presents activity factor scores for each category of activity). Then the trainer determines the number of hours spent in each category and calculates a point total for those categories. The sum of each weighted category is divided by 24 hours to calculate the WAF score.

The Final TDEE Score

To calculate our sample client’s TDEE, multiply her RMR score by the SAF or WAF score:


RMR = 1,459 kcal

SAF = 1.375; WAF = 1.130

TDEE = 2,006 kcal (SAF) or 1,649 kcal (WAF)

Mifflin-St. Jeor

RMR = 1,402 kcal

SAF = 1.375; WAF = 1.130

TDEE = 1,928 kcal (SAF) or 1,584 kcal (WAF)

With TDEEs ranging from 1,584 to 2,006, it’s easy to question the effectiveness of these calculations. After all, a 422-calorie differential equals a 154,030-calorie differential in a year—44 pounds. Obviously, these margins reflect differences in research methodologies and populations, but it is worth asking: Are they acceptable in light of the investments by clients and professionals alike? And do not forget how the potential for error is further compounded by subjective bias and the Hawthorne effect, which observes that people change their behavior when they know it’s being measured (New World Encyclopedia 2011). Finally, think about how much time you, as a trainer, would spend on these calculations. If it is not a billable service, is it really worth the effort?

Simpler Solutions

In light of these challenges, why not shift your initial focus away from outcomes—caloric balance—and toward the change process? A simpler approach can achieve your goals and help clients take charge of their actions and decisions. In his book Move a Little, Lose a Lot (Three Rivers 2009), James Levine, PhD, introduces a metabolic profile aimed at increasing nonexercise (NEAT) activities throughout the day. This tool lets you dump those unreliable 3-day activity logs and simply ask clients to list their typical Monday–Friday schedules from memory on a log similar to the one shown in Table 5.

This information can help clients identify the problematic areas of their day, times when they are sedentary and ways they could be more active. Adopting a semidirective coaching style, you can challenge clients to get moving at times when they typically sit still. Encourage simple, manageable tasks that build self-confidence and strengthen commitment to change. Also help clients build a process to evaluate the effectiveness of these NEAT challenges every week (Miller & Rollnick 2002).

For example, let’s say a client is working a 4-hour stretch at a computer terminal. Explore ways the client can increase NEAT during bathroom and water/coffee breaks (walking to more-distant bathrooms or water coolers) and at company meetings (walking meetings). After all, greater levels of NEAT promote greater weight loss (Levine 2009).

Point Systems

Another option is to develop a system that assigns points to all activities, similar to the Weight Watchers® approach. Assign a negative point for lying, reclining or seated activities (excluding sleep) and a positive point for standing activities; then incrementally increase point allocation for activities of greater intensities (e.g., 2 points for light-intensity activities like walking, 3 points for moderate-intensity activities such as light jogging, etc.). Add up the points clients attain in a day, and then coach them to examine where their points came from and challenge the clients to improve their scores.

These strategies shift attention away from hard-to-attain outcomes, like reducing calorie intake, and toward more manageable, positive and enjoyable processes that contribute significantly to sustained weight loss. Christopher Mohr, PhD, RD, owner of Mohr Results Inc., avoids caloric goals because he recognizes how unrealistic they are for most people. Instead, he and his wife, Kara Mohr, PhD, an expert in weight loss and behavioral change, focus on creating lifestyle change challenges for clients. Over time, this strategy helps people adopt healthier lifestyle habits without forcing them to count calories.

Nutritional Simplicity

No weight management program is complete without considering the dietary half of the energy balance equation. Here, too, we face similar challenges with self-reported data, the Hawthorne effect and the value of your time as a trainer. We have many options for tracking food intake and calories, ranging from free online databases (, and more) to a variety of quick and accessible mobile applications. Yet how reliable is this process if our ultimate goal is to quantify caloric intake in order to mathematically devise weight loss rate strategies?

Dietary exchange lists offer simpler ways to assess macronutrient and caloric intake. Used by many dietary professionals, these lists differ from the traditional USDA food groups in that foods are classified by macronutrient composition (protein, fats and carbohydrates) and caloric value rather than by origin (ADA & ADA 2011). Consequently, some foods shift to different categories (cheeses fall under the meat category and not under dairy, for example, on account of their macronutrient composition). Also, some caloric values used in exhange lists are approximate (caloric values were left out of Table 6 to avoid confusion with the Atwater scoring system used in the meal analysis). While this exchange system would certainly puzzle the public, health and fitness professionals can draw reasonably accurate estimates of macronutrient composition and caloric value while respecting scope of practice.

For more on using exchange lists and categorizing foods, visit the American Diabetes Association’s online store at to purchase Choose Your Foods: Exchange Lists for Weight Management, which retails for $3.25. Bear in mind, however, that using exchange lists to assess dietary intake from food logs is still labor-intensive and subject to the unreliability of self-reported data. Furthermore, an exchange list is not an interactive tool, so it cannot empower people to identify problematic eating patterns or to develop strategies for change.

Table 6. Dietary Exchange Lists

Sample Meal Analysis Using Exchange Lists

Easier Choices

Exchange-list numbers appear highly specific, but they are time-consuming to tabulate and still prone to error, which is why it can be more productive to shift your focus toward making healthier selections and controlling portion sizes. Although a general lack of understanding of standard portion sizes is a leading contributor to overeating, making healthier food selections can be equally challenging.

Many health and fitness educators can help people equate standard serving sizes with common household items, but educators often struggle with the complexity of coaching on food selections. NuVal® is a new nutritional scoring system that aims to simplify decision-making about the foods we eat ( Developed by an independent panel of nutrition and medical experts, this system ranks a food’s quality by assigning the food a single numerical score on a 1–100 scale. Higher scores reflect better nutrition.

The scoring algorithm considers 30-plus nutrients in the food—both good and bad—and boils them down to a single number ( 2011). This helps health and fitness professionals and consumers avoid one common mistake with weight management: eliminating problematic foods without considering deep-rooted triggers (such as emotions and previous experiences) that create cravings. NuVal may allow people to keep eating the types of food they crave, while seeking healthier equivalents.

There is another straightforward way to promote healthier eating in your clients: develop a simplified version of some existing and successful commercial programs that use a point system to build accountability and responsibility with eating habits. Once you are familiar with standardized portion sizes, create a food checklist that scores a positive point per serving of healthy foods (whole grains, vegetables, lean meats, and low-fat or nonfat dairy) and a negative point per serving of unhealthy foods (refined starches, fats, sweets, salty snacks).

Use a food-frequency questionnaire or general 24-hour dietary recall to collect information on typical eating habits, and then score and tabulate a typical day’s points. Use this data to help clients identify unhealthy choices and find ways to boost their daily scores. For example, a quarter-pound cheeseburger on a white bun with 16 ounces of regular soda could earn −6 points (−2 points for 2 ounces refined starch, −1 point for 1 ounce cheese, −1 point for high-fat meat, −2 points for 16 ounces of soda), whereas a healthy breakfast of Cheerios®, with 4 ounces skim milk and a medium banana, could earn 4 positive points.

The reality is that while obesity is a complex disease whose causes are not fully understood, we have many prudent, effective and simple solutions that can empower people to fight it. A visit to the National Weight Control Registry (NWCR), developed by James Hill, PhD, and Rena Wing, PhD, provides an aggregated databank of successful strategies for long-term weight loss and weight maintenance. A review of best practices within the databank shows that simplicity is a common thread in sustained weight loss (NWCR 2011).

We may feel overwhelmed and desensitized by the myriad quick-fix strategies that are advertised to satisfy the public’s need for instant gratification and overnight weight loss, but we must recognize the pitfalls of these empty promises. We need to adopt realistic, simplified approaches to weight loss that focus initially on processes rather than outcomes. The need and desire for change should be both important and relevant, and we must help clients overcome ambivalence and resistance while building their self-efficacy and commitment to change (Miller & Rollnick 2002).

Put aside the complicated numbers for now, and focus on coaching to engage, ignite and empower your clients.

Table 4. Individual Activity Factor Scores for Different Activities

No weight management program is complete without considering the dietary half of the energy balance equation.

Table 5. Sample 24-Hour Activity Log

Total 24-Hour Score: 27.05

WAF Score = Total ÷ 24 Hours: 1.13

  • Based on Atwater Factor Scores: 1 g carbs = 4 kcal; 1 g protein = 4 kcal; 1 g fat = 9 kcal.


ADA & ADA (American Diabetes Association and American Dietetic Association). 2011. Choose Your Food: Exchange Lists for Weight Management.; retrieved Nov. 21, 2011.

Ainsworth et al. 2011. 2011 compendium of physical activities: A second update of codes and MET values. Medicine & Science in Sports & Exercise, 43 (3), 1575–81.

CDC (Centers for Diseases Control and Prevention). 2010. Obesity Data and Statistics.; retrieved Nov. 21, 2011.

Frankenfeld, D., Roth-Yousey, L., & Comphere, C. 2005. Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: A systematic review. Journal of the American Dietetic Association, 105 (5), 775–89.

Hill, A.J. 2004. Does dieting make you fat? British Journal of Nutrition, 92 (Suppl. 1), S15–S18.

Levine, J. 2009. Move a Little, Lose a Lot. New York: Three Rivers.

Miller, W.R., & Rollnick, S. 2002. Motivational Interviewing (2nd ed.). New York: Guilford.

New World Encyclopedia. 2011.; retrieved Nov. 21, 2011.

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NWCR (National Weight Control Registry). 2011. Research findings.; retrieved Nov. 21, 2011.

Thompson, J.L, Manore, M.M., & Thomas, J.R. 1996. Effects of diet and diet-plus-exercise programs on resting metabolic rate: a meta-analysis. International Journal of Sports Nutrition, 6 (1), 4–61.

Weijs, P.J.M. 2008. Validity of predictive equations for resting energy expenditure in US and Dutch overweight and obese class I and II adults. American Journal of Clinical Nutrition, 88 (4), 959–70.

Whybrow, S., et al. 2008.The effect of an incremental increase in exercise on appetite, eating behaviour and energy balance in lean men and women feeding ad libitum. British Journal of Nutrition, 100 (5), 1109–15.

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About the Author

Fabio Comana, MA, MS

Fabio Comana, MA, MS IDEA Author/Presenter

Faculty Instructor for the National Academy of Sports Medicine (NASM), and faculty member in Exercise Science and Nutrition at San Diego State University, and UC San Diego. Previously, Fabio was an e...