BMI Is Broken – A 2,000-Year-Old Discovery Offers a Smarter Way to Measure Body Fat

Critics are once again questioning the efficacy of BMI as a tool for diagnosing obesity, suggesting that a more holistic approach to assessing health might be needed.

Instead of relying on this outdated metric, experts recommend using body fat percentage, a method inspired by Archimedes’ ancient principles, which offers a more precise measure of health risks associated with obesity.

Rethinking BMI: A New Year’s Resolution

Once again, the body mass index (BMI) is under scrutiny. This time, a group of experts commissioned by The Lancet is challenging its validity as a diagnostic tool for obesity. They argue that doctors should assess a patient’s overall health rather than relying solely on this flawed measurement.

BMI is determined by dividing a person’s weight in kilograms by the square of their height in meters. According to standard classifications, a BMI below 18.5 is considered “underweight,” while the “normal weight” range falls between 18.5 and 24.9. A BMI between 25 and 29.9 is categorized as “overweight,” and anything above 30 is classified as “obese.”

Given the significant health risks associated with obesity and even being overweight, one might assume that BMI is a well-founded and reliable metric. However, that assumption is misleading.

The Flaws of BMI in Health Assessment

Although people with higher body fat often have higher BMIs, the index itself is a poor diagnostic tool. One of its biggest flaws is its inability to differentiate between fat and muscle. This matters because excess body fat is strongly linked to heart disease risk, whereas BMI alone is not.

Recent research suggests that if obesity were defined by body fat percentage rather than BMI, as many as 15–35% of men classified as “non-obese” by BMI would actually be considered obese. This highlights BMI’s shortcomings and reinforces the need for more accurate ways to assess health.

However, it turns out that BMI both under- and over-diagnoses obesity. The same study found that up to half of the people that BMI classified as overweight and over a quarter of BMI-obese individuals were metabolically healthy.

Archimedes’ Insight: An Ancient Solution for Modern Health

BMI is clearly not an accurate indicator of health. Instead, it would be useful to access a direct measure of the percentage of body fat that is so closely linked to cardiovascular disease. To do that we need to borrow a 2,000-year-old idea from the ancient city-state of Syracuse on the island of Sicily.

Around 250 BC, Archimedes, the pre-eminent mathematician of antiquity, was asked by Heiro II, king of Syracuse, to help resolve a contentious issue. The king had commissioned a crown of pure gold. After receiving the finished crown and hearing rumors of the metalsmith’s less-than-honest reputation, the king worried that he had been cheated and that the metalsmith had used an alloy of gold and some other cheaper, lighter metal. Archimedes was charged with figuring out if the crown was a dud without taking a sample from it or otherwise disfiguring it.

The illustrious mathematician realized that he would need to calculate the crown’s density. If the crown were less dense than pure gold, he would know the metalsmith had cheated. The density of pure gold was easily calculated by taking a regularly shaped gold block, working out the volume, and then weighing it to find its mass. Dividing the mass by the volume gave the density. So far, so good.

Archimedes’ Principle: A Revolutionary Approach to Measuring Body Fat

Weighing the crown was easy enough, but the problem came when trying to work out its volume, because of its irregular shape. This problem stumped Archimedes for some time, until one day he decided to take a bath.

As he got into his extremely full tub, he noticed that some of the water overflowed. As he wallowed, he realized that the volume of water that overflowed from a completely full bath would be equal to the submersed volume of his irregularly shaped body. Immediately he had a method for determining the volume, and hence the density, of the crown.

Vitruvius tells us that Archimedes was so happy with his discovery that he jumped straight out of the bath and ran naked and dripping down the street shouting “Eureka!” (“I have found it!”) – the original eureka moment.

Sadly, it is unlikely that this is actually how Archimedes solved the problem. Instead, it is more likely that Archimedes used a related idea from hydrostatics (the mechanical properties and behavior of fluids that are not in motion), which would later become known as Archimedes’ principle.

The principle states that an object placed in a fluid (a liquid or a gas) experiences a buoyant force equal to the weight of fluid it displaces. That is, the larger the submerged object, the more fluid it displaces and, consequently, the larger the upward force it experiences. This explains why huge cargo ships float, providing the weight of the ship and its cargo is less than the weight of water they displace.

Using this idea, all Archimedes needed to do was to take a pan balance with the crown on one side and an equal mass of pure gold on the other. In air, the pans would balance. However, when the scales were placed underwater, a fake crown (which would be larger in volume than the same mass of denser gold) would experience a larger buoyant force as it displaced more water, and its pan would consequently rise.

Measuring Body Fat: Archimedes’ Legacy in Modern Health Metrics

It is precisely this principle from Archimedes that is used when accurately calculating body-fat percentage.

A subject is first weighed in normal conditions and then reweighed while sitting completely submerged on an underwater chair attached to a set of scales. The differences in the dry and underwater weight measurements can then be used to calculate the buoyant force acting on the person while under water, which in turn can be used to determine their volume, given the known density of water.

Their volume can then be used, in conjunction with figures for the density of fat and lean components of the human body, to estimate the percentage of body fat.

While it clearly isn’t as easy to use as the basic BMI measurements, and there may be better ways to assess body fat, this 2,000-year-old trick can certainly provide a more useful assessment of health risks.

Written by Christian Yates, Senior Lecturer in Mathematical Biology, University of Bath.

Adapted from an article originally published in The Conversation.

Never miss a breakthrough: Join the SciTechDaily newsletter.
Follow us on Google and Google News.