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Satyajeet Vispute
Mar 11, 2020

Hydrostatic weighing for body fat estimation is a means of analyzing the fitness of a person. We shall understand its principle of working, and highlight the steps used in calculating an individual's body fat percentage, through it.

It is believed that Archimedes came up with his principle by observing water being displaced as he got into his bathtub. The story goes, that he got so excited by his discovery, that he forgot to dress, and ran stark naked through the streets, shouting "Eureka"!

Surely the Greeks want the world to be fit. First, they inspired us all by building life-like sculptures of their Gods displaying muscled and toned bodies in all their heavenly glory. Then, one of them went ahead and conceived a mathematical equation which forms the working principle of what is deemed by many as the 'gold' standard of body fat measurement!

Hydrostatic body fat measurement is based on the principle of water displacement thought up by Archimedes, an ancient Greek mathematician and physicist. It is known to give an accurate measurement of the body fat percentage of an individual. In the following lines, we shall find out how hydrostatic weighing for body fat measurement actually works.

To understand the working principle of hydrostatic weighing, we first need to learn about buoyancy, or the ability of an object to float on a liquid.

So what exactly decides if an object floats or sinks? The most apparent answer would be its weight. The heavier the object, the more likely it is to sink.

But then how is it that large ships which weigh tons are able to float, while a pebble which weighs only a few grams still sinks? It is because ships is much larger in size, and so are capable of displacing a larger amount of water than a small pebble can.

Archimedes understood this fact, and so stated that it's not the weight of a body, but the weight of water that it displaces which decides its buoyancy. If the weight of water displaced by a body is more than the weight of the body itself, then it will float, otherwise it will sink.

Clearly, this implies that smaller-sized objects with larger weights (denser objects) will sink. Now, considering the composition of the human body, bones and muscles being denser, are prone to sinking, while fat being less dense, will float.

While swimming, a person uses his hands and feet to push the water away from his/her body, that is, displaces it to stay afloat. A skinnier person, while swimming, will have to put in a larger effort to displace more water to stay afloat than a heavier person having more body fat.

Thus, we arrive at the conclusion that, people with a higher body fat percentage weigh lesser in water than the people who have a higher percentage of bones and muscles in their bodies. This fact forms the working principle of hydrostatic weighing.

Hydrostatic weighing is also known as underwater weighing. The following is its two-step procedure.

To calculate the body density of a person, a few measurements have to be taken. First, the person is weighed on dry ground. This weight is noted down as the person's Dry Weight.

Then, his/her lung's residual volume RV is calculated. RV is the amount of air remaining inside a person's lungs after complete exhalation. RV can be measured by using diluted helium or oxygen techniques, or can be calculated by measuring the vital capacity of a person, and multiplying it with 0.24 for males, and 0.28 for females.

Next, the person is asked to enter a special weighing tank. It contains a specially designed weighing chair, which is submerged in water. The chair is connected via a transducer to a digital computer, which calculates the weight of the person sitting on it.

The person is required to completely exhale, and then sit on this weighing chair inside the tank. It is important that he/she is fully submerged along with the chair for this process to work.

After sitting still for about 5 - 10 seconds, the computer is able to measure the person's weight. This underwater weighing process is repeated 4 - 5 times, and an average of all the obtained values is calculated. This average is noted down as the person's Wet Weight.

Once all these values are obtained, they are put in the following hydrostatic weighing equation, which gives the value of a person's body density.

**Body Density = Dry Weight ÷ [((Dry Weight - Wet Weight) ÷ Water Density) - RV - 0.1]**

Note that all the values used in this equation are measured in kilograms, and RV is measured in liters. In the previous equation, the factor 0.1, which is subtracted along with RV, accounts for the remaining volume of air present in the person's gastrointestinal tract.

To calculate body fat using the body density measured in the previous step, either the Brozek formula or the Siri formula is used.

The following lists out both these formulae:

*Siri Formula:*

**Percentage Body Fat = [{4.95 ÷ Body Density} - 4.50] × 100**

*Brozek Formula:*

**Percentage Body Fat = [{4.570 ÷ Body Density} - 4.142] × 100**

1) The biggest source of error in hydrostatic weighing is the calculation of RV. This RV measures the volume of air remaining in the lungs after complete exhalation.

The greater the value of RV, the higher a person's buoyancy, and therefore, his/her weight underwater comes out to be lower. Hence, it needs to be subtracted from the body density calculation. However, accurate calculation of RV is difficult, and this introduces errors.

2) Both the Siri formula and the Brozek formula assume the density of fat-free body mass to be constant, but in reality, its value varies from person to person. Hence, the actual calculated body fat percentage in lean persons is slightly higher, while in obese people it come out slightly lower.

Hydrostatic weighing is a reliable and close-to-accurate method for calculating a person's body fat percentage. It has been effectively used for a long time, and for all practical purposes, gives an accurate reading of the amount of fat within a person's body.