Does your ponytail splay outward or droop limply?

Raymond E. Goldstein, a professor of complex physical systems at the University of Cambridge in England, does not have a ponytail, but he has been pondering the physics of the hairstyle for a couple of years.

He and two other physicists have been trying to determine whether the shape of a ponytail can be deduced from the properties of a single hair. After all, a head with 100,000 strands is a complex physical system, as anyone with a copious coiffure can attest.

And it turns out that there is a simple theory. The crucial characteristics are elasticity, density and curliness, which essentially tell how springy a piece of hair is, plus the length of the ponytail. The researchers came up with a simple formula that describes the ponytail shape when the hair is bundled together.

They called it the Rapunzel number. “We couldn’t resist,” Dr. Goldstein said.

A short ponytail of springy hair, characterized by a low Rapunzel number, fans outward. A long ponytail with a high Rapunzel number hangs down, as the pull of gravity overwhelms the springiness. “I think we were surprised about the simplicity of this,” Dr. Goldstein said.