# 26 Body Density

# Body Fat Percentage from Body Density

Health care professionals, (like registered nurse Jolene introduced in the previous Unit), understand that BMI provides a relatively quick way to asses body composition and and monitoring changes, but it does not always accurately capture a person’s body composition. Body fat percentage can provide a more complete picture of body composition, but we know from the previous unit that theskinfold method of determining body density often exhibits relatively high uncertainty. Lower uncertainty can be achieved by actually measuring body density, and using empirical models to interpolate body fat percentage (BF%) from body density (). Different equations have been developed for males and females in different populations in order to improve accuracy, but the following is once example: ^{[1]}. In order to understand those models we first need to understand density and how it can be measured.

# Body Density

## Mass and Volume

In order to understand density and how it might be measured, we first need to understand mass and volume. Volume (V) is the amount of space taken up by an object. Mass (m) can be defined two ways. First, it is a measure how strongly an object attracts other objects by gravitation (gravitational mass). Second, it is a measure of how much an object resists being accelerated (inertial mass). As far as physicists can tell, all objects have the same value for inertial mass and gravitational mass. Atoms are the matter that make up everyday objects like the body, and each type of atom exhibits a certain mass, so we sometimes speak of the mass as a measure of the amount of matter in the object, and that is reasonable in everyday situations. For example, if you were to count out carbon atoms, then together they would exhibit a mass of 12.011 grams measured either gravitationally or inertially. The seemingly odd number of atoms is known as *Avogadro’s Number *and the mass (in grams) exhibited by that many atoms of a particular type is known as the atomic mass. The number at the bottom of each square in the periodic table tells you the atomic mass. We won’t be finding the mass of objects by couting up numbers of atoms. Instead we will find the mass by measuring gravitational attraction or resistance to acceleration.

## Density

The SI units for volume and mass are cubic meters (**m ^{3}**) and kilograms (

**kg**). Mass Density (ρ), which we usually shorten to just density, for any object is defined as its mass divided by its volume. The same mass of different materials will have different volume, and thus different densities. For example one

**kg**of foam takes up much more space than one

**kg**of steel (in fact, about 80 times more). This giant table of material densities is a useful reference (click the

*to see the values in SI units).*

**kg/m**button^{3}### Reinforcement Exercises

Sometimes when looking up density you will see weight density listed instead of mass density, in which case weight rather than mass is divided by the object volume. As we will see in the following chapters, quoted weight densities are only valid on Earth, while mass densities are more generally valid. The following chapters will explain how we measure the volume, weight, and mass of a body in order to calculate body density for use in estimating body fat percentage.

### Reinforcement Exercises

- Siri, SE (1961), "Body composition from fluid spaces and density: analysis of methods", in Brozek J, Henschel A (eds.), Techniques for measuring body composition, Washington, DC: National Academy of Sciences, National Research Council, pp. 223–34 ↵

method for measuring body fat percentage using specially designed calipers to measure the thickness of skinfolds that are pinched from several specific locations on the body as inputs to empirical equations

relation between the amount of a material and the space it takes up, calculated as mass divided by volume.

mathematical explanation of the relation between measured values that is used for making predictions

a quantity of space, such as the volume within a box or the volume taken up by an object.

a measurement of the amount of matter in an object made by determining its resistance to changes in motion (inertial mass) or the force of gravity applied to it by another known mass from a known distance (gravitational mass). The gravitational mass and an inertial mass appear equal.