I heard on the radio this morning that all salaried employees were working for free today because in a Leap Year February has an extra day.  The assumption was that salaries are annual and based on a standard 365 day year.  Therefore a Leap Year must have one extra work day.

I understand the logic, but the unquestioning acceptance of this statement as fact immediately caught my attention.  Something quite obvious to the mathematically literate has been missed.  So I Googled the question “how many work days does a year have?” To my amazement, the vast majority of websites that attempted an answer also got it wrong.  First of all, they all obsessed over the differences caused by different approaches to holidays.  That’s understandable, but beside the point.

Let’s look at the math.  There are not exactly 52 weeks in a typical year.  There are 52 weeks AND one day in 365 days.  So there are not necessarily 104 weekend days in a calendar year.  71% of the time there are 104 weekend days, and 29% of the time there are 105 weekend days.  Not one of the websites I visited seemed to get this.  So a typical calendar year has EITHER 260 or 261 work days, ignoring holidays of course.

So, what does happen with working days in a Leap Year?  Well, there are at least 104 weekend days, so there could be 262 working days.  But there could be 105 weekend days, in which case there may still be only 261 working days.  But wait!  There could be 106 weekend days, as in the case of a year in which January 1 is a Saturday.  In that year, there would be only 260 working days.  That’s right – you might work fewer days in a Leap Year than you did the non Leap Year before!

How can this be?  It is the result of mapping a seven day week on a calendar year that never has an even multiple of seven.  Mathematical patterns are wondrously complex and endlessly fascinating.  What a great example of how math affects our everyday working lives!