How many seconds in a leap year, and the four-year average?

Question

Solve in your head. How many seconds are in a leap year (366 days)? And what is the average number of seconds per year over a four-year cycle with one leap year? Aim: under 30 seconds.

Accepted Answer

Leap year. A non-leap year has 31{,}536{,}000 seconds. A leap year just adds one more day: 31{,}536{,}000 + 86{,}400 = 31{,}622{,}400 	ext{ seconds.} (Directly: 366 	imes 86{,}400 = 365 	imes 86{,}400 + 86{,}400 = 31{,}622{,}400.) Four-year average. Over four years there are three common years and one leap year, so the average simply adds one extra day spread across four years, 86{,}400 / 4 = 21{,}600 seconds per year: 31{,}536{,}000 + 21{,}600 = 31{,}557{,}600 	ext{ seconds per year on average.} Cross-check the long way: \dfrac{3 	imes 31{,}536{,}000 + 31{,}622{,}400}{4} = \dfrac{94{,}6…

How many seconds in a leap year, and the four-year average?

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