How To Calculate The Volume Of A Person

"Eureka!" shouted the ancient Greek philosopher and mathematician Archimedes when he found a solution to the gnarly problem of measuring the volume of the king's crown. The king wanted to know if the crown was made of pure gold, and to determine that, Archimedes needed to know its density, which requires a determination of the volume. Emerging from the bathtub, he went running through the streets in elation because he had just realized that the amount of water he displaced in the tub was equal to the volume of his body. He could use the same procedure to measure the volume of the crown.

Anyone can use Archimedes trick to measure the volume of their body, but there's an even easier way. All you have to do is weigh yourself because the density of the average human body is a known quantity.

If you want to imitate Archimedes and measure the volume of water your body displaces in the bathtub, you need an accurate way to make the measurement. One way is to fill the tub to the brim, collect the water that overflows when you submerge yourself and transfer it to a graduated container. To make sure you collect all the water, you'll probably have to construct a funnel or drain that directs water into a bucket rather than onto the floor.

A better way would be to draw a line on the side of the tub and fill the tub to that line. Make sure the line is high enough to allow you to immerse your entire body, including your head. When you're underwater, have a helper mark the new water level. The distance between the lines is the depth of the water you displaced, and when you multiply this by the length and width of the tub, you get the volume of the water – and your body.

If you're an average human being, the density of your body is about 8.3 lbs/gal (1010 kg/m³), which is a little less than seawater but a little more than pure water. That's why you float in the ocean but not in your bathtub. You can use this value for density to calculate the volume of your body as long as you know your weight. Here's the procedure:

1. Weigh Yourself

Get the most accurate results by weighing yourself before getting dressed.

2. Divide by Density

Density "d" is defined as mass "m" divided by volume "V."

\(d=\frac{m}{V}\)

Solving for V, we find that:

\(V=\frac{m}{d}\)

3. Convert to Units of Your Choice

Use one of these conversion factors:

1 cubic meter = 264 U.S. gallons = 1,057 quarts = 33,814 ounces = 35.31 cubic feet.

​Example:​ Phil weighs 155 pounds. To calculate the volume of his body, divide by the average density of the human body in pounds per gallon:

\(155\text{ pounds}\frac{1\text{ gallon}}{8.3\text{ pounds}}=18.41\text{ gallons} = 2.43\text{ cubic feet} = 0.07\text{ cubic meters}\)