How many seconds in a year?

Question

Solve in your head. How many seconds are in a (non-leap) year? Give the exact figure. Aim: under 20 seconds.

Accepted Answer

Build the day first: 24 	imes 3600 = 86{,}400 seconds per day. Then split 365 = 300 + 65: - 86{,}400 	imes 300 = 25{,}920{,}000 - 86{,}400 	imes 65 = 86{,}400 	imes 65. Route: 864 	imes 65 = 864 	imes 60 + 864 	imes 5 = 51{,}840 + 4{,}320 = 56{,}160, so 86{,}400 	imes 65 = 5{,}616{,}000. 25{,}920{,}000 + 5{,}616{,}000 = 31{,}536{,}000 	ext{ seconds.} Takeaway. The famous mnemonic: a year is \pi 	imes 10^7 seconds (31.4M vs. the true 31.5M, accurate to 0.4\%). For Fermi work, use 3 	imes 10^7; for exact work, anchor on 86{,}400 s/day, a number worth knowing cold.

How many seconds in a year?

Your answer

More Mental Math questions