# Approximation to the number of seconds in a year?

Is there any mathematical formula which shows that there are approximately $\pi \times 10^7$ seconds in one year. I understand that the pi is probably due to the earth's circular orbit, but am not sure where the rest could come from .

• $\pi$ has nothing to do with it. Where did you find that? To find the number of seconds in a year, multiply 1 year by 365.25 days by 24 hours by 60 minutes by 60 seconds. Commented Sep 21, 2014 at 14:54
• I know, but pi*10^7 is sometimes given as a rough approximation to be used if you dont have a calculator Commented Sep 21, 2014 at 15:00
• Commented Sep 21, 2014 at 15:00
• It works fine, but it seems to be a coincidence, unlike, say, the distance the Earth travels in one year. Commented Sep 21, 2014 at 15:01
• **Why does a nano century equate to $\pi$ seconds? ** Either cesium atoms know about earth's trajectory around sun, can compute $\pi$, and play a trick on us. Or... This is an (approximate) coincidence. Fait vos jeux... Commented Sep 21, 2014 at 15:44

It's a unit conversion: $$1\,{\rm yr}=\frac{365\,{\rm days}}{\rm year}\times\frac{24\,{\rm hrs}}{1\,{\rm day}}\times\frac{3600\,{\rm sec}}{1\,{\rm hour}}=3.1556926\times10^7\,{\rm sec}$$ Since $3.1557$ is (somewhat) close to $\pi\sim3.1416$, we use the approximation you cite.
Technically, the year is actually 365.25 days long, so using that gives a slightly better approximation that gets one to $3.15576\times10^7\,{\rm sec}$, though most sources I've seen simply use 365 days. Both values are still less than half a percent off of the $\pi\cdot10^7$ value.