What are the Best Basal Metabolic Rate Equations?

If you want to estimate your daily energy expenditure in order to calculate your energy needs for weight gain, weight loss, or athletic performance, you first need to estimate your basal metabolic rate: how many Calories your body burns at rest.

Your basal metabolic rate (BMR) tells you how much energy your body burns to just “keep the lights on” – it’s the energy used to power the basic functions of your vital organs, to accomplish sufficient protein and cell turnover to keep your tissues functioning properly, etc. If you didn’t leave your bed all day, and didn’t move a muscle, your basal metabolic rate is the amount of energy you’d still burn in a day. ¹

To estimate your BMR, you just need to plug some basic demographic and anthropometric information (like height, weight, age, sex, and/or fat-free mass) into a formula, and the formula will spit out an estimate of your BMR. So, which equation should you use?

When you dig through the research on the topic, you’ll find a lot of proposed equations for estimating basal metabolic rate. In fact, a 2013 study found 248 different BMR equations, and there are doubtlessly many more that have been published since then. But, there are two that generally perform the best in most populations.

If you don’t know your body-fat percentage, the Oxford/Henry equation(s) are your best bet. If you do know your body-fat percentage, the 1991 Cunningham equation is generally the way to go.

The Oxford/Henry Equations are as follows:

The 1991 Cunningham equation, on the other hand, is the same for everyone:

BMR = 21.6 × Fat-Free Mass (kg) + 370

Or

BMR = 9.8 × Fat-Free Mass (lb) + 370

If you don’t know your fat-free mass (FFM), but you do know your body-fat percentage, you can calculate your fat-free mass using this equation:

FFM = Body Weight × (1 – Body-Fat Percentage)

Why are these the two best equations in most populations?

Oxford/Henry

The Oxford/Henry Equations were developed using the most data, and they have the strongest support in subsequent research.

Back in the 1980s, the UN and the World Health Organization wanted to develop equations that could be used to estimate energy expenditure in a diverse array of populations. Global food insecurity and malnutrition were even bigger problems then than they are now, and obesity rates were starting to trend up in developed nations, so developing accurate equations to predict BMR (which could then be used to predict total energy needs) seemed like a pressing concern.

The resulting FAO/WHO/UNU equations (sometimes referred to as the Schofield equations) are still frequently used, but they have one significant problem: they reliably tend to overestimate BMR, especially in smaller people.

These equations were developed from a database consisting of data from 7,173 subjects, but nearly 50% of the data (from 3,388 subjects) came from just 9 old Italian studies that were conducted between 1936 and 1942. And, as it turns out, one of two things is true: either 1) Italians during this era had exceptionally high basal metabolic rates, or 2) Italian fascists weren’t particularly good at doing metabolism research.

In 2005, researchers re-examined the FAO/WHO/UNU equations, the underlying data used to develop these equations, and the additional data that had been published during the intervening decades. They found that, compared to research in virtually all other populations, the Italian subjects had BMRs that were about 10% higher than other populations with the similar characteristics. Since those Italian subjects were relatively small, and massively overrepresented in the database used to develop the FAO/WHO/UNU equations, they’re the primary reason why the resulting equations were subsequently found to overestimate BMR, especially in smaller people. The image below illustrates this divergence in young women, but similar differences were observed for other age and sex cohorts.

So, the researchers excluded those non-representative Italian studies, added data from an additional 7,000+ subjects from studies published between 1985 and 2005, and updated the equations using a larger (10,552 total subjects) and more representative sample that wasn’t unduly influenced by any overrepresented subpopulations. This is a much larger population than the samples used to develop other popular BMR equations using height, weight, and age, such as the Harris-Benedict equation (239 subjects), the revised Harris-Benedict equation (337 subjects), and the Mifflin-St Jeor equations (498 subjects).

Since the Oxford/Henry equations were developed, a meta study found that the Oxford/Henry equations had the best combination of low error (small average deviations between measured and predicted BMRs) and low bias (not systematically over- or under-estimating BMR in particularly large or particularly small people) across both sexes. Similarly, another huge study with nearly 17,000 subjects found that the Oxford/Henry equations were among the best-performing equations for people in all BMI categories. Finally, a 2022 meta-analysis found that the FAO/WHO/UNU equations performed best in people with overweight and obesity, but that review included relatively few studies that used the Oxford/Henry equations. However, BMR estimates provided by the FAO/WHO/UNU equations and the Oxford/Henry equations tend to converge at higher body weights and BMIs (in other words, if the FAO/WHO/UNU equations perform well in people with obesity, the Oxford/Henry equations do too).

Overall, in most populations, the Oxford/Henry equations are the best BMR equations based on height, weight, age, and sex.

Cunningham, 1991

Much like the Oxford/Henry equations, the 1991 version of the Cunningham equation is the result of synthesizing data from multiple other studies. Cunningham had first developed an equation for estimating BMR from fat-free mass in 1980. In the intervening decade, more research groups investigated the relationship between fat-free mass (FFM) and BMR, allowing Cunningham to systematically analyze the results from a total population of 1482 subjects. The studies included both males and females, with a pretty even mix of lean and obese subjects.

Subsequent research has supported the validity of the 1991 Cunningham equations. For instance, a decade after Cunningham’s study, Wang and colleagues analyzed the FFM/BMR relationship in the published research (which included another seven studies that came out after Cunningham’s equation was published). It was a somewhat less rigorous analysis – I don’t believe they applied weightings based on the number of subjects in each study – but it found that the “average” equation to predict BMR from FFM was BMR = 21.5 * FFM + 407, which is practically indistinguishable from Cunningham’s equation.

Furthermore, they modeled the theoretical relationship between FFM and BMR that was revealed from animal research spanning a range of 7 orders of magnitude; when scaled to body size, metabolic rates are shockingly consistent and predictable between species. Wang and colleagues found that the theoretical relationship between FFM and BMR in animals of all sizes could be modeled with this equation: BMR = 21.7 * FFM + 374². Again, that’s virtually indistinguishable from the 1991 Cunningham equation.

Finally, to lend support to both the 1991 Cunningham equation and the Oxford/Henry equations, both equations produce comparable BMR estimates. Essentially, if the Oxford/Henry equations are good, and the 1991 Cunningham equation produces similar estimates, that suggests that the 1991 Cunningham equation is also pretty good (and vice versa). Using the NHANES body composition cohort, I calculated the estimated BMR for all participants using both the Oxford/Henry equations and the 1991 Cunningham equation. They produced estimates that differed by less than 100 Calories, on average.

Which equation should you use?

If both the Oxford/Henry and the 1991 Cunningham equation are generally good, and typically produce similar BMR estimates, which one should you use?

If you don’t have a decent idea of your body composition, the Oxford/Henry equations are probably the way to go. However, if you do have a pretty good idea of your body composition, the 1991 Cunningham equation is likely the better option. Fat-free mass is by far the most important predictor of BMR. Equations like the Oxford/Henry equations work well because sex, height, and weight are reliably associated with fat-free mass. So, in essence, the Oxford/Henry equation is tacitly predicting your fat-free mass to then predict your BMR. But, if you think you can estimate your body-fat percentage with a reasonable degree of accuracy (within about 5% or so), using the 1991 Cunningham equation essentially lets you go “straight to the source,” and estimate BMR directly from FFM.

Ultimately, the choice of equation shouldn’t make that large of a difference for most people, most of the time. There are a few exceptions, however.

First, if you think your body-fat percentage is considerably higher or considerably lower than average for people of your age, height, weight, and sex, the 1991 Cunningham equation is likely a much better option than the Oxford/Henry equations. If you’re 15% body fat, and the average person of your height, weight, age, and sex is 30% body fat, the Oxford/Henry equations would likely underestimate your BMR.

Second, if you’re over 60 years old, the Oxford/Henry equation corresponding to your age and sex is probably the better option. The relationship between fat-free mass and BMR remains fairly stable through most of your adult life, but BMR per unit of fat-free mass begins declining more rapidly past the age of 60 (which we’ll discuss in more detail later in this series). So, the 1991 Cunningham equation would likely reliably overestimate your BMR.

Third, if you’re an athlete, both of these equations are likely to underestimate your BMR. As we’ll discuss later in this series, athletes tend to have considerably higher BMRs than non-athletes, even when accounting for differences in body size and body composition.

Just how accurate are these equations?

Even though the Oxford/Henry and 1991 Cunningham equations are the cream of the crop, don’t expect them to perfectly nail your BMR. As discussed in a previous MacroFactor article, even the best BMR equation can produce relatively large under- or over-estimates. You can be reasonably confident that the value produced by these equations will be within about 150-200 Calories of your actual BMR, and you can be quite confident that the value produced by these equations will be within about 300-400 Calories of your actual BMR. In other words, if these equations estimate that your BMR is 1600 Calories per day, there’s about a two-thirds chance that your actual BMR is between 1400-1450 Calories on the low end, 1750-1800 Calories on the high end, and a 95% chance that your actual BMR is between 1200-1300 Calories on the low end, and 1900-2000 Calories on the high end.

Final notes

You may know the 1991 Cunningham equation as the Katch-McArdle equation. They’re the same equation. It was developed by Cunningham, and popularized by Katch and McArdle in their exercise physiology textbook. Since it was developed by Cunningham, I’m giving him the credit.

If you’re only semi-confident in your ability to estimate your body composition, there’s no problem with calculating your BMR using both the Cunningham and Oxford/Henry equations, and averaging the two values.

The Mifflin-St Jeor equation deserves an honorable mention. For formulas based on height, weight, age, and sex, I think it’s probably the second best, after the Oxford/Henry equations.

Finally, if you’d like to learn more about the determinants of basal metabolic rate, to better understand the (surprisingly cool) theory and physiology underpinning these equations, you’ll really enjoy the next article in this series. Subsequent articles in this series will also discuss how factors like age, sex, and weight loss impact BMR, and we’ll wrap it up by using all of that data to improve on the BMR equations covered in this article. We’ve already published a BMR calculator with these new equations that you can try out for yourself, but the articles explaining the rationale methodology used to develop our new BMR equations will be published over the next three weeks. Stay tuned!

1. There are several different terms that describe similar but slightly different concepts, including basal metabolic rate (BMR) or energy expenditure (BEE), sleeping metabolic rate (SMR) or energy expenditure (SEE), and resting metabolic rate (RMR) or energy expenditure (REE). For the purpose of this series, we’re using all of these terms interchangeably. Technically, this series is mostly about RMR/REE, which is the amount of energy your body actually burns at rest most of the time. BMR is the amount of energy you burn first thing in the morning, and measuring BMR requires subjects to sleep in the lab overnight. Sleeping metabolic rate is, quite intuitively, the amount of energy you burn while sleeping, which also requires subjects to sleep in the lab overnight. BMR is usually a little lower than RMR, and SMR is usually a little lower than BMR, but all three values scale with each other (i.e., you’re not going to have a really high RMR and a really low SMR), and most research on the topic assesses RMR since the subject burden of measuring RMR is much lower than BMR or SMR. RMR is also more broadly representative of your “normal” metabolic rate, since most people spend most of their time awake. The reason we opted to use the term “BMR” is just that it’s the term that more people are familiar with, and these terms are all used interchangeably by most non-academics. ↩︎
2. The actual equation is a nonlinear allometric scaling equation. This is the linear approximation corresponding to the range of FFMs typical in humans. ↩︎