Accurate and Easy Bodyfat Determination

First placed on the Internet February 2003

Many people who are interested in following a healthy lifestyle have interest in knowing their "body fat" content. A new very simple method of getting an amazingly accurate value is available.

It is a fact that (body)fat floats in water and bone and muscle sink. Our bodies are a combination of various items like this and most of us have an average density very close to that of water. If we learn what our average body density is extremely precisely, we can accurately know how much of us is actually bodyfat!

It is commonly accepted that "lean" body tissues, such as muscles are more desirable from a health viewpoint than the fatty tissues we all have in our bodies. We have no interest in getting into any debate regarding whether that premise is true or not. This presentation is merely to present a very simple, accurate, and inexpensive method of accurately determining the numerical bodyfat percentage value.

Show Baton This system is based on using a set of precision weights (Batons) and Floats to increase or decrease our flotation in a swimming pool, by a factor of about 1/1000. When a person selects one of the many Batons or Floats, he/she would then either sink, float or hover in a standard swimming pool. Your goal is to achieve 'Neutral Buoyancy'. These Batons and Floats are so precise that in less than five minutes of an enjoyable activity, a person can determine the average body density to better than one part in a thousand. That is a remarkable accuracy, especially for such a simple and easy procedure. Ah HA! Do you see the point? With that great accuracy, say you REALLY behaved yourself for JUST ONE WEEK regarding whatever diet you want to use. When you test yourself again a week later, if you even made an improvement of only one part in a thousand, you would see it! Big smile, and WONDERFUL motivation regarding sticking with the diet! Psychologists call this "immediate positive feedback" which reassures you that eating those NASTY foods is really paying off! And you don't have to wait many months to see any results, a single week often does it!

(This system also works great for kids, and the competitive aspects of being a "game" to compete with a friend or sibling gives a brand new incentive for kids to be more aware of junk food and their diet and exercise. This photo is from a Public Service Announcement [PSA] that we made for combating Childhood Obesity, which is why the picture is of kids!)

At the bottom of this presentation are links to several different ways you can do this. Several of them are things you could make or buy for surprisingly few dollars total. The Analysis Charts and Progress Charts are provided here, too, for free! We even provide a computer calculator so you see your accurate results immediately.

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This presentation was first placed on the Internet in February 2003. At least 147,000 people have read about this concept since then. Since we do not charge for this information, we have no way to know how many people have made sets of the necessary items, but we are pretty sure that at least several thousand have, including at least one Medical Doctor, who indicated that he felt he could help his obese Patients with it.


As we began researching this subject, we were surprised to discover that there seems to be remarkably little actual scientific basis for any ABSOLUTE figures for bodyfat percentage! There is EXTENSIVE research that has been done to evaluate many different concepts of determining a number to represent bodyfat percentage. That suggests that the various systems are adequately evaluated, but that the actual bodyfat numbers produced could possibly ALL be slightly high or low! Since we approached this subject from the perspective of a Physicist, we apparently have applied an entirely new approach to bodyfat determination!

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We note that the human body is made up of a variety of different components, and its composition can be described in different ways. The body could be described in terms of the VOLUME of the various components. We might also narrow it down to only those descriptions that describe WEIGHT percentages rather than VOLUME percentages, we could describe a human body in chemical terms as being: around 60% water; 15% proteins; 20% lipids (fats) with the remaining 5% being mostly carbohydrates with small amounts of many nucleic acids included. A more common description is: around 14% bone; 6% blood; 40% muscle; 20%+ fat; 10% organs; with the remainder being assorted other parts. (This description is usually described simply by the fat percentage, called the Bodyfat percentage, which is the figure that is usually desired.) These different types of components each have their own different densities and they each compose different percentages of the body as indicated above. Blood generally has a density very close to sea water, of slightly over 1.0 gm/cc, slightly more than fresh water. Bone has a much higher density. Fat has a density well below 1.0, around 0.918 gm/cc, and its substantial quantity is why most people can float in a swimming pool (particularly when they fill their lungs with air, which has even lower density).


There are several popular methods that have been available for determining bodyfat percentage. As is common in marketed products in America, amazing claims are made in their ads. Unfortunately, only one of these methods has been shown to be of significant value (or accuracy)! It is commonly described as Hydrostatic Weighing, and has long been universally considered the "gold standard" of available methods, because all experts agree that it is far more accurate than any of the other methods that are commonly used. (Accurate in this sense means that repeated testing can give very similar results). That procedure is expensive, time-consuming, extremely uncomfortable, and even potentially dangerous! Under some conditions, hydrostatic weighing has given inaccurate results, and a discussion below explains why that was possible and how to avoid such errors.

A comment should be made about "precision" or "accuracy" as every product is presented as having unbelievably good performance! The correct attitude is to have a scientific approach, which is based on the repeatability of results. This cannot be known from a single measurement, or even a small number of measurements. But if the measured results of ten or twenty or fifty (blind, or double-blind) tests (on the same person, near the same time) are analyzed statistically, a "probable error" value is obtained. For the hydrostatic weighing method, that Probable Error is generally much less than ±1%. This implies that if ONE measurement is done, it is likely to be accurate to within ±1% (with the considerations regarding air and gases within the body as discussed below). When such statistical analysis has been done regarding bodyfat calipers or bioelectric impedance or the other (inexpensive) alternatives, the probable error has nearly always been greater than ±10%. Very few actual scientific studies have been done regarding such products, but some have even suggested that ±15% is not unusual. This implies that if ONE measurement was done, the value obtained IS LIKELY TO BE off (in either direction) by that large value. With such terrible accuracy, getting a reading of 19% (a nice result!) could actually mean 34% (seriously obese) or 4% (professional athlete). Pretty much a meaningless result, except for being able to brag about a 19% bodyfat content!

Marketing people recognized that millions of people are health conscious, and that they would certainly have interest in knowing some number that would describe their own bodyfat content, as related to their personal program of healthy living. As a result, a number of products keep coming onto on the market. They have each sold very well, due somewhat to exaggerated claims regarding their accuracy, but in reality, all the inexpensive ones have been relatively worthless!

Skinfold Calipers (or Anthropometric Modeling)

The most common, and the least expensive, is a simple clamp-like device (often referred to as bodyfat calipers) that is used to grasp loose skin (sometimes also called a skinfold measurement) commonly done near the waist. (Experienced testers take measurements from several different locations on the body and take several measurements from each location, but that seems to be rare regarding the use of the popular devices.) The premise is that the amount of skin that can be grasped is an indication of "flab" and therefore bodyfat percentage. Such devices generally have a scale that allegedly reads directly in percent bodyfat. One aggressively promoted product claims a precision of being within ±1.1% of the Gold Standard method! Don't count on it! Highly respected researchers have found that the average error for the skinfold procedures, even using the multiple locations and multiple tests each, tends to be between ±10% to ±15%. A person who gets a reading of 20% with such a device might feel comfortable that they are physically fit and healthy. That conclusion would likely be true if the reading was accurate! Unfortunately, that well established research confirms that the readings of such devices are commonly off by as much as ±15%, and usually off by around ±10%. Therefore, that person above might ACTUALLY have a bodyfat content of as low as 5% (a professional athlete) or as high as 35% (considered obese). Any reading from such a device is therefore meaningless, only because its accuracy is so poor. It turns out that there are many, many different things that can affect how much skin can be grasped in such a device, which have little to do with fitness or bodyfat content.

Such devices always come with a disclaimer that the accuracy obtained is dependent on the skill of the tester. That is certainly true! An experienced tester gets an initial idea of an expected bodyfat percentage just from a brief look at the client. When a tester gets a reading that is very different from what he or she expects, the tester just repeats the test. He or she keeps grabbing skin folds until they get a result that is in line with what they had estimated by first looking at the person! This becomes somewhat similar to the guy at the County Fair who claims to be able to accurately guess your weight! He is often pretty accurate, but it is due to his observational skills. A "good" caliper bodyfat tester shares those skills, in closely estimating ahead of time what the correct value should be, and then tests to get a result that matches that. The device becomes somewhat secondary!

The Skinfold Caliper equations on which these devices are based were originally derived from the simplest (and least accurate) of the Hydrostatic Weighing equations (given below), the Siri 2-compartment model. There appears to have been a single product that attempted to use a more accurate 4-compartment equation model, but no reliable analysis of that is yet available. It seems likely that the large errors that generally occur in the caliper usage would overwhelm the fact that the equations are more accurate.

Skinfold testing is variously performed on the chest, abdomen, thigh, triceps, subscapular, midaxillary, and calf regions. If a tester only measures one of those locations, and only once or twice, it is a sign that little actual understanding of that system is present, and that any results would be as poor as indicated above.

However, higher qualified testers (who seem to be rare) make measurements in several or all of these locations, and even multiple measurements in several or all of these location, in order to then use an appropriate formula, either Williams (men or women), Jackson-Pollock (men or women), or Tran-Weltman (men or women). When done very thoroughly like this, accuracy of skinfolds can be improved to a level that is useful. Those six different formulas can provide results of moderate repeatability. The Tran-Weltman formulas are slightly different, based on girth (waist) measurements rather than skinfold.

Scientific research based on these multiple measurement methods by skilled testers established that the Jackson-Pollock formulas gave a 95% confidence level (two Statistical Standard Deviations) range of ±9.6% to ±15.3%; and the Williams formulas gave an equivalent confidence level range of ±10.3% to ±15.6%. This means that even in the hands of highly skilled testers, and with the multiple measurement procedures, the bodyfat number produced by skinfold calipers could commonly be around ±10% or ±15% wrong! More significantly is that the results were generally wrong in the same direction, giving lower results than was likely actually the case. The Jackson-Pollock results were consistently 5.9% low and the Williams results were consistently 3.3% low, in other words, giving unrealistically pleasant answers!

Imagine how incorrect the results would be when someone does a quick single pinch of skin!

BIA - Bioelectrical Impedance Analysis (BIA)

Another popular product is usually a little more expensive, and it has an electrical premise as its argument. It is often called a Bioelectrical Impedance Analysis. An electrode is held in each hand, or against the wrist or ankle (or similar arrangement) and a very small electric current is passed through the person's body, and the electrical impedance (like resistance) is measured. The premise is that bodyfat conducts electricity at a lower rate than does lean body tissue. That claim might actually be true, but it turns out that there are many other things that affect a person's measured body resistance. Simply washing the hands makes a great difference, and thoroughly scrubbing them even more, as this removes the skin oils (and outer dead layers of skin) that generally create a lot of electrical resistance. Body conductivity is tremendously affected by hundreds of other effects. If a person drinks an (effective) electrolyte solution (akin to Gatorade or most sports drinks), body conductivity can rapidly increase, which reduces body resistance. Such effects have been well documented to cause this method to also regularly be off by as much as ±15%. The discussion above indicates why this very large error range makes any results from this method virtually worthless.

BMI or Body Mass Index

There are other products or systems being sold that similarly attempt to use indirect methods to determine bodyfat content. One called the Body Mass Index (or BMI) doesn't even try to determine body fat percentage. It simply is a formula based on a person's weight and height (and gender) that claims to give accurate results. The person's weight in kilograms is divided by the square of the height in meters! I am 200 pounds or 91 kg. I am 6'2" or 1.88 meters. So 91 / (1.88)2 is 25.7 which would be my BMI. Anyone looking at the diversity of people can quickly tell that it could not actually be credibly accurate for all people. There are pairs of people with identical heights and weights, one of whom is extremely muscular and fit (and therefore has high body density) who seems somewhat skinny, and the other of whom is flabby and out of shape (and therefore has much lower body density) who seems pudgy. The BMI approach cannot distinguish between these two extremes, so it is even worse for people in between.

In general, all these (convenient and inexpensive) alternatives to hydrostatic weighing have extremely poor accuracy, so poor that any results are virtually meaningless. The only accurate methods necessarily involve actually accurately determining the average body density of a person. Only a few approaches have been used. Some are extremely technological, involving millions of dollars of medical equipment! The DEXA (Dual-Energy X-Ray Absorbtiometry) method uses two different types of X-rays to penetrate the body, to distinguish between different densities of tissues, an interesting process but so expensive that it has not been used very extensively. By far the most available of the really accurate methods is the "Gold Standard", the Hydrostatic Weighing, submersion method.

Bod Pod Chamber Method

We will take a moment to comment on one other method, which has only recently become available. One variant of this approach has been heavily promoted, which is called the Bod Pod.

Since a lot of people do not want to get wet in order to accurately know their bodyfat content, a novel new approach has appeared. On first glance, it seems very promising. It is a very rigid chamber, smaller than a phone booth, which a person gets into. Once inside, the entry door is sealed tight, so no air could get in or out. Then, very briefly, either a pump adds or removes a small, accurately measured, amount of additional air to or from the chamber, and the air pressure change inside the chamber is accurately measured. The air pressure is therefore briefly changed by the addition or removal of that amount of air. This slight change of air pressure, if really precisely measured, would give the ratio of air space inside that chamber (excluding the volume of the person) to the volume of that precisely added burst of air. Some simple math could then determine the remaining (empty space) amount of AIR surrounding the person, and then subtracting that volume from the known volume of the chamber, the person's volume can then be known and then combining this with the dry body weight, the average body density can be calculated fairly easily.

The original volume of the chamber is accurately known, so the Ideal Gas Law (pressure times volume is constant at = nRT) gives the desired result! Say that exactly 1.000% (of the entire chamber volume) of the air in the chamber is removed, and the measured pressure dropped by exactly 2.000%, it would indicate that the remaining air in the chamber must now be half of the original entire chamber volume, and so the person inside is taking up half the volume of the chamber. This is because the 2% rise in pressure would have only been a 1% rise without the person in there. In any case, it is an interesting idea. However, there are some problems. The equipment is extremely expensive, on the order of $30,000. Accurately measuring the pressure change is a minor problem because for the sake of the comfort of the person the pressure is not changed too drastically, and EXTREME accuracy is important. Introducing exactly a specific amount of air into the chamber is far harder. Air density is greatly affected by room temperature and even relative humidity, so accuracy could be much worse under certain conditions. Since the reading needs to be accurate to much better than one part in about one hundred thousand (for decent accuracy of the results), the precise performance of the air pump, the air temperature, and many other variables must be carefully accounted for.

The sensation of having the air pressure in the chamber change by 1% is about like being in a very fast elevator that suddenly moves around 20 stories in a building. If the chamber volume was about 22 cubic feet (620 liters) and a (200 pound) person who takes up 3 cubic feet uses it, the pressure change would be about 1.16%, or the equivalent of a 25-story elevator ride, where the ears might give the popping sensation with that rather sudden change of air pressure. If a 300-pound person got in, the remaining volume would be around 4/5 so the pressure would about 1.25%, which is closer to the equivalent to about a 30-story elevator ride. The chamber cannot be made too small to keep large people from possibly experiencing ear damage!

To be of value in determining an accurate bodyfat number, that CHANGE of pressure must be measured extremely accurately. IF it can be measured to one-part-in-one-hundred, in other words, to an actual pressure accuracy of 0.0001% or so, a useful and repeatable average body density and therefore a useful bodyfat number can be obtained. However, notice that 0.0001% is one part in a million regarding the accuracy of measuring the 14.7 PSI of the atmospheric pressure! That is almost a thousand times more precisely than a quality barometer is able to measure! If the pump had removed an amount of air that was even a few millionths different, the readings become nearly useless! (For comparison, the Hydrostatic Method and our Baton method are each roughly ten times more accurate than that!)

Put another way, if the measured pressure difference is 1.00000% due to the pump with no one in the chamber, and the (accurate) 1.15789% difference with our 200 pound person in it, if that person exhales to alter his body volume by one part in a thousand, his body volume changes from 3.00 cubic feet to 2.997 cubic feet then the reading should be 1.15771% decrease. This difference, which both Hydrostatic weighing and our Baton method can measure, represents a DIFFERENCE in the measured pressure of 0.00018%, or under two parts in a million in the pressure reading!

As indicated, that technology seems as though it MIGHT have some value. However, the present ways it is used are so crude as to not really (yet) be of significant value.

An interesting sign of this exists! The procedure of using the Bod Pod system never involves the person trying to exhale all the air they can! But it would be really critical to do so, exactly as in Hydrostatic weighing! And that is very simple to see. As a person exhales, his/her abdomen moves inward, which is a clear indication that the person is then taking up less volume of space! Since it is SO critical to determine that volume to extreme accuracy, around one-part-in-a-thousand, to accurately determine the bodyfat number, even slight differences in the amount of air in the lungs can greatly alter the bodyfat readings, exactly as we discuss regarding the Hydrostatic and our systems. But it is a sign that even the makers of the Bod Pod devices must not realize how important it is to exhale all that air. Their equipment is simply not accurate enough to even measure such effects as are needed!

For their information, it would be necessary to know the precise amount of air removed from the chamber to about one part in five hundred thousand, an extremely difficult thing to do, and then they would need to measure the change in pressure to a precion of around 0.0008" of water column, far more accurately than most equipment can measure.

The equipment is so expensive that very few places have it, and they generally charge around $50 to $60 for each test. Probably not worth pursuing!

The device described above would inject about 1/2 gallon volume of additional air (1.7 liter) into that chamber, an amount that would need to be accurate to better than one part in four thousand. If the pump and mechanism happened to lose an amount of air equivalent to the size of a single Cheerio in releasing it into the chamber, that could seriously affect the results!

This method, if done really accurately, (repeatably with similar results) which is not really realistic with current equipment, would still have the error effect of amount of air inside the person, in the lungs and in the intestine, as discussed below regarding the Hydrostatic Weighing method. If the person did not expel all the air possible from the lungs, the body would have a volume that was larger by that amount of air that could be expelled, and so the resulting average body density calculated would be wrong by that factor. Ditto regarding intestinal gases. So even with the high expense of this method, it really does not overcome any of the possibilities of error factors of Hydrostatic Weighing, and only provides a DRY method and one that does not involve being strapped to a heavy chair and lowered under a pool for 45 seconds at a time ten times! Something to say for those advantages, but not regarding its poor accuracy!

DEXA or Dual-Energy X-ray Absorbtiometry

We should mention that there is a Medical X-Ray method that also exists, which is only available in hospitals. That method has the potential of extremely accurate results, as long as all the X-ray shadows are interpreted correctly as being bone, muscle, fat, blood, etc. And, as long as correct values are then used for the actual densities of the items in those X-Ray shadows. But it is well known that the density of bones in athletes and black men are significantly different than for white women, for example. The person evaluating such X-Rays must apply several assumptions. It also seems not worth pursuing, although the equipment is so complex and expensive that it does not ever figure to become a reasonable cost alternative.

Research by Snead and others has established that the DEXA approach gives distressingly different results for many older persons, which seems related to the DEXA approach's difficulty in accurately assessing soft tissue densities.

The DEXA method generally requires around 12 minutes of time of X-Rays with the pencil-beam mode, with a total radiation exposure of around 10 millirems. Very few test-retest research experiments have been done, but the results suggest that the DEXA method has around a ±1% repeatability of bodyfat results, when analyzed by the same trained investigator. However, the DEXA results generally were different from 4-compartment model bodyfat determinations by an average of ±5.3%. The consistency of results suggests that the method may have potential, but the ±5.3% difference from commonly accepted results, and even greater differences in the elderly, suggests that the analysis is not yet adequate. The 95% statistical confidence range (two Statistical Standard Deviations) for DEXA results suggests a range from ±7.8% to ±10.5% bodyfat percentage, not very impressive.

The DEXA Method involves around a million dollars of equipment, which probably will not be regularly tied up in attempting to determine the bodyfat number for many individuals!


Back to the Hydrostatic Weighing!

It is well known that fatty tissue has a lower density than lean tissue or bone or even water. It happens that bone and lean tissues have higher density than (fresh) water while fat has a somewhat lower density than (fresh) water. As a result of the fact that we all contain some amount of fat, nearly everyone will float in fresh water. We even float higher up in water that has salt in it, because salt water has a higher density than fresh water, which makes our bodies even more relatively buoyant.

Fresh water, as in a swimming pool, has a density (or specific gravity) of 0.9978 gm/cc, at around 72°F. (In case you are curious, seawater has differing amounts of salinity, but the density is around 1.026 gm/cc.) (And technically, the water in a swimming pool might be thought to have a density of 1.0000 gm/cc, but that is only true if the water is at a temperature of 39°F.) Human body fat has a density of 0.918 gm/cc. Human muscle tissues, human blood, human bones and all the other component parts of us have their own densities. It would be great if those values were precisely known, and many are. But it has been found, for example, that athletes and African-Americans happen to have slightly higher density bones than average. It would also be great if we knew the exact percentages of bone, blood, and the rest are in our bodies. But there are variations here, too. Some people are "big-boned" and others are "barrel-chested" or "thin-as-a-rail". These factors all affect the relative proportions of the component materials of us. The point being: even the best analysis has a certain error factor. It works out that these variations among people seem to have a collective effect of well under ±1% regarding bodyfat analysis. This is actually why the hydrostatic weighing method can have a repeatable accuracy of better than ±1%.

Fortunately, the proportions of bone and lean muscle tissue in an individual non-body-builder are fairly consistent, and the proportion of blood in our bodies seems to be fairly consistent, too. Therefore, even though bone is more dense and we have different components of many different densities, it is possible to establish a generalized "non body fat" body density value. Since the accuracy and repeatability of individual readings is very good, a person could "chart" the progress of a program of physical maintenance.

We will describe two different procedures here of hydrostatic weighing. First, we will discuss the long-used method that involves the person being strapped to a chair and submerged, which has developed the reputation of being so accurate and reliable that it has now become the Gold Standard method. (Isn't that what they did to witches in Salem???) Then, we will describe a variation of that same method that is just as accurate but far simpler, less expensive, more comfortable, and safer.

The Gold Standard - Hydrostatic Weighing

A person is generally charged between $30 and $40 each time they want to use this method to determine their bodyfat content. The procedure generally takes around an hour to complete, and a health club or YMCA must have staff occupied with this procedure, and the equipment is extremely expensive, so lower fees are not realistic. A strong chair is suspended by a cable and hoist and an accurate weighing scale over a swimming pool or similar tank. The swimming pool must not have anyone else swimming in it during that hour, since wave disturbances would push the chair around and disturb the scale readings. Most reputable operations also have a Medical EMT nearby, but that tend to keep that person out of view, so as not to scare the person too much! The person is thoroughly strapped to the chair, not unlike an electric chair! This can be extremely stressful to the person, especially when they realize that they are about to be lowered beneath the water, for around 45 seconds. Just before the person's head goes below the surface, he/she is told to expel ALL the air in their lungs, and then the chair is lowered further so the person and chair is fully submerged.

An extremely accurate weight scale (usually around 1/3 ounce precision) is attached to the cable, (in a dark humor detail, it is sometimes an autopsy scale!) which measures the underwater weight of the combination chair/person. Generally, it takes around 30 seconds for waves and chair motions to stop enough to get a constant reading on the very sensitive scale. After a reading is obtained, the chair is raised back above the surface. The person has been underwater for around 45 seconds, AFTER having expelled all the air possible, and he or she often coughs and gasps as soon as the mouth is above the water. This procedure, with empty lungs, is extremely stressful physically. It is also very stressful mentally, as the person generally fully realizes that his/her life is completely dependent on the person operating the equipment and the proper functioning of all the equipment. If even the slightest thing binds up or otherwise goes wrong, the person has very serious problems regarding survival. Health clubs generally require a person to sign a legal waiver (lots of fine print) prior to this procedure!

Having this done once would be bad enough! But it turns out that even by 1969, Katch discovered that there is a "practice curve" of the person expelling air to the greatest amount. Generally, this whole process needs to get repeated around seven times, with the effect of the underwater weight increasing by between 7% and 10%, BEFORE useful data can even be collected! Generally, THEN the results from the final three runs are considered accurate and they are averaged to determine the best value for the body density.

Slight variations on how well a person expels air from the lungs tends to have significant effects on the results, so this has become the accepted method of doing the testing, repeating this whole process from seven to ten times, which generally takes around an hour to accomplish. Personally, I am somewhat amazed that people PAY $30 to $40 to have this done to them!

However, the results are very accurate, generally better than ±1% repeatability. Some scientific studies (Bemben) have shown that the test-retest resulting body density figures have a statistical variance of around 0.005 gm/cc. The person described above who would get a 20% value could be confident that the actual bodyfat was likely to be between 19% and 21%, which represents very useful information.


The results of Hydrostatic Weighing is not actually a Bodyfat Percentage, it is actually a value related to the Average Density of the Body. There are two procedures that are then generally done to process that number. The first step is usually in recognition of the fact that there is always some amount of air remaining in the lungs, even when a person tries to expel all of it. That amount is called the Residual Volume, and it is variable but is generally considered to be about 1.2 liters (for an adult). The measured value of the Average Body Density then gets increased due to this factor (as a proportion of the total body volume or displacement). This factor generally results in multiplying the measured Body Density by about 1.013 to get the lung-air-corrected value of Body Density, (Db).

At this point, an assortment of assumptions need to be applied to convert this Body Density value into a number that describes Bodyfat Percentage. It turns out that there are many different formulas that have been developed to make this conversion. One of the first, and still one of the most popular is called the Siri 2-compartment model. It is based on the assumption that the human body is made up of just two types of material: fat-mass (FM); and fat-free-mass (FFM); and that the two are assumed to have average densities of 0.900 kg/cc and 1.100 kg/cc respectively. Further, it is assumed that the relative amounts of the three major components of the FFM (aqueous, mineral and protein) are also known as defined, and that they are constant and the same in all individuals.

Most of these assumptions have been shown to be inaccurate to various extents. However, the Siri 2-compartment model happens to be a very simple equation, so it has maintained great popularity. The Siri (2-compartment) formula is: (4.95/(body density) - 4.50) *100 which gives a percentage number that is claimed to be the Bodyfat Percentage.

This formula certainly is a simple way to produce numbers of Bodyfat Percentage, but careful scientific study has been done on such formulas, and it has been found that the Siri 2-compartment formula gives results that have a 95% confidence interval ranged from ±8.1% to ±12.0% bodyfat percentage, for different ages and genders studied, as compared to methods that are considered to give reliable results. This means that the numbers produced by the Siri 2-compartment model can often be ±12% high or low. A value that is given by Siri at 20% could therefore actually reasonably be 32% (rather obese) or 8% (professional athlete).

Considering how good the Hydrostatic Weighing method is to start with, it is rather sad when the formula used introduces such large possible errors! Children and older people have been well proven to have different characteristics that affect the accuracy of any 2-compartment model. A number of gender and ethnic differences are also well proven.

There are other formulas that have been presented to provide more accurate results. They tend to be 3-compartment and more models, where the body is seen as being a more complicated combination than just the two of fat-mass and fat-free-mass. There is a Siri 3-compartment model that has greatly improved accuracy. Some 4-compartment models, particularly Heymsfield and Baumgartner, are seen as extremely reliable.


The gold standard method has always been by far the most accurate method for determining bodyfat content. In fact, it has generally been the criterion on which nearly all other systems are evaluated! But it has a number of disadvantages. For a health club to buy the equipment, often more than $10,000 is involved. In addition, extremely trustworthy staff members must operate the equipment, necessarily realizing that if they get absent-minded the person could die, and they require substantial training to correctly and safely operate it, and also to then determine the actual results, although some systems now use computers to do that. A health club must also consider the potential liability issues, as some people panic when completely helpless underwater strapped to that chair, and CPR and other medical attention has known to have been necessary. It does not seem to be publicized, but this procedure is rarely allowed for elderly people, possibly because of the extreme physical stress involved. In this, it has worked out to be an advantage that generally only very fit, athletic people tend to have such serious interest in bodyfat content to be willing to pay $30 to $40 to have it measured. Each person must pay a significant amount of money, and experience substantial discomfort, in order to get these results.

As we see it, these disadvantages tend to discourage people from going through this procedure more than once! This greatly limits the value of the results. We believe that if people could get that level of accuracy, but inexpensively and without physical and mental trauma, they would be likely to repeat the measurements at weekly or monthly intervals. They could then CHART their own changes in bodyfat content due to exercises and/or diet. We see that as far more useful. In this regard, a modified version of the gold standard is described next.

New Method, Modified Gold Standard

Showing How to Hold Baton First, you weigh yourself, in just your swimsuit, with an accurate scale. For our discussion, let's say that is 180 pounds. Next, have available a precision set of specialized weights (we call them Batons) and Floats, and go to a nearby swimming pool. A friend needs to come along as an observer. Without needing to know how to swim you get in the shallow end of the pool. Lift your feet up and curl up in a tight ball. A friend will usually see that you are floating, with part of your back exposed above the water. This is hard for you to sense yourself, since we have relatively few nerve endings in our back and it is not very sensitive to many things. This is why the friend needs to be there.

Now, you do the exact same thing, except this time, you first exhale ALL the air you possibly can before doing it. You may still float, but now your friend will notice that you float lower in the water, or you will now sink. This is because you do not have all the buoyancy of the air in your lungs increasing your "displacement" of water, and so your average body density has now increased. It may now be much closer to the density of the water (if still floating) or even above it (if sinking). There is still some air in your lungs, which cannot be expelled, but there are mathematical adjustments that can be made to correct for that.

Next, your friend will hand you one of the precision Batons or Floats, A Baton if you were still floating or a Float if you were sinking. You will now do the exact same procedure, exhaling all the air you can, and curling up in a tight ball, but now you will be holding the Baton or Float against your belly. Depending on which size Baton or Float she handed you, you may now (a) sink to the bottom; (b) remain floating with part of your back out of the water; or (c) float just below the surface, or very slowly sink or rise.

Notice that you only have to be underwater for a very few seconds, and that you are not strapped to anything, and that you are in the shallow end of the pool. At any moment, you could just stick your feet down to the bottom and instantly get your head above the water. You do not even need to know how to swim, as you stay in the shallow end of the pool!

Batons in Rack The first time you would do this, you may need to try several different of the precision Batons or Floats, but after a few tries, you would know which specific Baton or Float was close to correct for you. You could then do this several times, each time trying to expel more air from your lungs. The more you can expel, the more likely you would sink with a specific Baton or Float. If you find that you can learn how to expel enough to clearly sink, you might try the next lighter Baton or bigger Float. (A lighter Baton or a bigger Float will give a lower bodyfat percentage number.) Your friend would make notes about each try.

What you are really accomplishing here is creating "neutral buoyancy". The combination of you and that specific precision Baton or Float then has exactly 0.9978 gm/cc density of the water mentioned above, identical to the water. Since the Baton weight or the Float buoyancy is already accurately known, some simple algebra gives your Average Body Density, and therefore Bodyfat Percentage directly. We have even already done the algebra for you!

Now get out of the pool because we are ready to get the results!

Down below are described several different sets of the precision Batons, along with a set of similar precision Floats, each of which comes with one or more "Analysis Charts", where all the algebra has already been done for you. We have also now provided a web-site calculator (linked below) that takes your dry body weight and the Baton/Float letters you used to calculate your bodyfat. Let's say that you found that you (180 pounds as above) could have neutral buoyancy with the 'D' precision Baton. On the Analysis Chart, you would just look at the column "180 lbs" and go down to the row "D" and find 30.5% (By the way, that represents 54.9 pounds of body fat, 30.5% of 180!) That is actually there to enable you to survive for quite a while if it would ever turn out that no food was available. Some people obviously could survive longer than others! You might note that if you can avoid floating with the next lighter Baton, the 'C', your bodyfat would be 30.2% instead, so you are determining your Bodyfat Percentage to within about ±1/3%!

Here are guidelines from the American Council on Exercise

WomenMen
Essential fat10-12%2-4%
Athletes14-20%6-13%
Fitness21-24%14-17%
Acceptable25-31%18-25%
Obese32% up26% up

So, such a value would be considered Obese for a man , but barely Acceptable for a woman.

There are adjustments that we have included here but not mentioned yet: the actual average non-fat density of various body-types of humans; and the fact that there is residual air in both the lungs and the stomach/intestine.

As to the second consideration, the Results Charts have been adjusted to account for an expected 1.2 liters of air that cannot get expelled from the lungs as well as a reasonable average of intestinal gases.

As to the first effect, very little data is really yet available on how large the effects are. Professional athletes and blacks are known to have bones that have higher density, and bones represent around 14% of body weight. These effects certainly exist, and our web-page calculator accounts for them, but we believe that practical use of this method eliminates the need for such an adjustment! You really are not as interested in your bodyfat percentage as compared to other people, as you are small changes that might occur due to changes in your diet and/or exercise routines. If you regularly measure your bodyfat percentage with this method, such as every week, such inter-person effects would not apply (for one individual person) and any changes noted in your bodyfat percentage should be extremely accurate. That would enable reliable and accurate knowledge regarding the effects of changes in your exercise routines or your diet. That is really what is important!

You might have noticed in this just how small these density effects actually are. This explains why we float much higher in seawater, because its density is greater than fresh water. Actually, our example man above would be buoyant by nearly five pounds more in seawater than in pure freshwater. The calculations would have to be considerable adjusted, if he had done his measurements in the ocean!

And, with that great an effect just between fresh water and seawater, you might better see how critical it is to expel all the possible air out of the lungs, and how even very slight differences can greatly affect the results.

It has been well established with the gold standard method that it is best if the person eats similar meals before each such measurement, in order to get the most precise results. It was found that if a person ate a meal that created a lot of intestinal gas in the hours before testing, the results can be significantly affected! The more similarly you prepare yourself each time, the more reliable any changes will be. Between those things and practice at expelling air from the lungs, you should be able to get repeatable measurements that are consistent within ±0.5% regarding any changes that happen in your bodyfat percentage.


Here are the versions:

You can actually get a ball-park number for your bodyfat percentage without making these things, which is likely to be within about ±10% of your actual bodyfat number. You need a swimming pool and a friend!

Have a "normal" amount of air in your lungs, NOT having severely exhaled or inhaled. And then simply float stationary! Your friend sees (or maybe even measures) how much of your head sticks out of the water! If you do NOT float and sink toward the bottom, your bodyfat is likely to be around 13% or lower. If your friend sees TWO INCHES of the top of your head above the water, you are likely to be around 24%. If your friend sees about FOUR INCHES (essentially to the very top of the earlobes), you are likely to be around 40%. If around SIX INCHES (essentially to the earholes, and your eyes are above the water) then you are likely to be around 57%. You might see from the large changes in bodyfat numbers due to rather small differences in the amount of the head being visible, that this method is only very approximate, with ±10% being expected. It only provides a ball-park number!

We mention this because there are a LOT of people who have been told that they have 8% or 4% or 11% bodyfat, due to using the extremely inaccurate bodyfat caliper method or electrical impedance (methods absolutely proven to regularly be ±15% off either way, so in other words, meaningless except for bragging purposes.) A person could try to alter this method by intentionally normally exhaling first, which makes you float around one inch lower, which would appear to give an estimate of around 6% lower. By attempting to exhale all the air you can, you can lower your body by about 3 inches, which can give the appearance of around 16% lower estimate. The point is that by simply altering the amount of air in your lungs, you could change this reading by as much as 16%, another indication of why the far more accurate and repeatable Batons and Floats is desirable. If you really want to believe that you are at 8% or 11% so you can brag to your friends, there are many ways you can create such a number. However, if you actually want a REAL number for bodyfat, this very crude method can get you within about ±10%, and the Batons-Floats can get you within about ±1%.


The main presentation page on a simplified Hydrostatic Weighing system is at: Accurate and Easy Bodyfat Determination

Combating Childhood Obesity Through Motivation (specifically directed at Childhood Obesity)

The Simple and Accurate Bodyfat Measurement - PSA Storyline of the 30-second and one-minute PSA (Public Service Announcement) TV presentations.

The page that provides the PVC construction details for the Batons and Floats and all the printable Analysis Charts is at:
Bodyfat Analysis Weights - Filled PVC Plastic Batons http://mb-soft.com/public2/bodyfwp2.html

The page that provides the construction details for the Pepsi bottle-based Batons and Floats and all the printable Analysis Charts is at:
Bodyfat Analysis Weights - Pepsi Bottles and Pennies! http://mb-soft.com/public2/bodyfwp3.html

The page that has the Determining Your Accurate Bodyfat Percentage Automatic Calculator which uses the Baton/Float letters and the dry body weight


This presentation was first placed on the Internet in February 2003.


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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago