Science Puzzle
How Much Hair Do You Grow in a Day?
Your hair grows all the time, so slowly that you never see it happen. But there's a lot of it.
Imagine collecting one day's growth from every hair on your head and laying all those tiny bits end to end. Without looking anything up, can you estimate how long the line would be: a few centimetres, a few metres, or more?
The Answer
About 30 to 40 metres a day: longer than three buses parked end to end. You can get there with two rough guesses and one sum.
First guess: how many hairs? A patch of scalp about 1 centimetre square holds roughly 200 hairs, and a scalp covers very roughly 500 square centimetres. That gives about 100,000 hairs, which matches the usual figure for most people.
Second guess: how fast does a hair grow? If you've had a haircut, you'll know hair grows about a centimetre a month. That's roughly a third of a millimetre a day.
Now multiply: 100,000 hairs × a third of a millimetre is about 33,000 millimetres, or roughly 33 metres, every day. Over a year that's more than 10 kilometres of hair.
This is called a Fermi estimate, after the physicist Enrico Fermi, who loved them. At the first atomic bomb test in 1945, he dropped scraps of paper as the blast wave passed, watched how far they were blown and estimated the bomb's power. His answer was within a factor of about two of the measured value. The trick is to break an impossible-looking question into small steps you can make sensible guesses about. Errors in the guesses tend to partly cancel out, and the answer usually lands within the right ballpark, good enough to tell centimetres from metres from kilometres.
The principle: Estimation. Breaking a big unknown into smaller quantities you can reasonably guess, then combining them, gives a surprisingly reliable rough answer.