Calculating the number of cells in the human body is tricky. Part of the problem is that using different metrics gets you very different outcomes. Guessing based on volume gets you an estimate of 15 trillion cells; estimate by weight and you end up with 70 trillion. Carl Zimmer at National Geographic explains:
So if you pick volume or weight, you get drastically different numbers. Making matters worse, our bodies are not packed with cells uniformly, like a jar full of jellybeans. Cells come in different sizes, and they grow in different densities. Look at a beaker of blood, for example, and you'll find that the red blood cells are packed tight. If you used their density to estimate the cells in a human body, you'd come to a staggering 724 trillion cells. Skin cells, on the other hand, are so sparse that they'd give you a paltry estimate of 35 billion cells.
How did these researchers come up with 37.2 trillion? They actually broke down the number of cells by organs and cell types, going through the literature available to come up with a detailed list of volumes and densities in everything from intestines to knees. So, for example, there are 50 billion fat cells in the average body and 2 billion heart muscle cells. Adding all those up, they got 37.2 million. (This doesn't include any of the millions of microbes living on you, by the way.)
The authors point out that this isn't simply a good pub trivia question. Using cell counts, and comparing them to the average, can help doctors identify problems. "Knowing the total cell number of the human body as well as of individual organs is important from a cultural, biological, medical and comparative modeling point of view," they write.