Do We Really Only Work One Day a Year?

There’s an old joke that claims to prove mathematically that we only work one day a year. It sure doesn’t feel that way, but is the math correct? 

Here’s the breakdown according to Jokes Place:

So you want a day off? Let’s take a look at what you are asking for!

There are 365 days this year.

There are 52 weeks per year in which you already have 2 days off per week, leaving 261 days available for work.

Since you spend 16 hours each day away from work, you have used up 170 days, leaving only 91 days available.

You spend 30 minutes each day on coffee break. That accounts for 23 days each year, leaving only 68 days available.

With a one hour lunch period each day, you have used up another 46 days, leaving only 22 days available for work.

You normally spend 2 days per year on sick leave. This leaves you only 20 days available for work.

We are off for 5 holidays per year, so your available working time is down to 15 days.

We generously give you 14 days vacation per year which leaves only one day available for work and I’ll be damned if you’re going to take that day off!

That can’t possibly be right! Let’s break it down.

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  • There are 365 days this year. So far so good! We’ll disregard leap years.
  • There are 52 weeks per year in which you already have 2 days off per week, leaving 261 days available for work. Obviously this joke works on the assumption of a 9 to 5 office job. A lot of people don’t have that luxury, but we’ll work with it. Also, if Jan 1 falls on a weekend it’d be 260 work days, but we’ll stick with 261 to make it easier.
  • Since you spend 16 hours each day away from work, you have used up 170 days, leaving only 91 days available. Close, but not quite. 16 hours out of 261 days is equal to 174 days, leaving 87 days. This doesn’t seem right, but keep in mind we’re counting all 24 hours in a day. 87 x 24 = 2088 hours; dividing by 52 weeks works out to 40.15 hours per week. So far so good.
  • You spend 30 minutes each day on coffee break. That accounts for 23 days each year, leaving only 68 days available. I wish! I’ve only ever been allowed a 15-minute break, but let’s assume our hypothetical boss is more lenient. The math goes totally off the rails here. 23 days is equal to 552 hours or 1104 half-hours. That’s 3 years of breaks! Even if you assume that “days” in this case refers to 8-hour work days instead of full 24-hour days, that’s including breaks on days off (23 work days = 184 hours or 368 days worth of breaks), and it then subtracts full days instead of work days. What we really need to do is multiply 2.5 hours/week by 52 weeks to figure out how much time is lost to coffee breaks. That’s 130 hours, or 5 days and 10 hours. From our 87 days, we’ve got 81 days and 14 hours left.
  • With a one hour lunch period each day, you have used up another 46 days, leaving only 22 days available for work. Again, this is three years worth of lunch breaks or uses the same conflicting definitions of days (including weekends). Realistically, most people wouldn’t subtract anything at this point because they either have to clock out for lunch or have that hour built in to a 9-hour schedule, so it would have already been subtracted in the 16 hours a day of not working. But what the hell; there are some lucky bastards in this world. 5 hours a week, 52 weeks a year is 260 hours or 10 days 20 hours. 70 days and 18 hours to go!
  • You normally spend 2 days per year on sick leave. This leaves you only 20 days available for work. Nope! We’re working with different definitions of days here. You can’t straight-up subtract two full days at this point; we’ve already taken out the hours you aren’t at work or are taking a break of some sort. If we’re assuming a 6.5 hour work day at this point, we’re still at 70 days, 5 hours.
  • We are off for 5 holidays per year, so your available working time is down to 15 days. Same as above. Subtract 32.5 hours; there are 68 days 20.5 hours left.
  • We generously give you 14 days vacation per year which leaves only one day available for work… And again! Odds are that “two weeks” vacation is really only 10 work days plus associated weekends, but even assuming that you really do get 14 full (6.5 hour) work days off, that’s only 91 hours. That leaves us with a whopping 65 days and 1.5 hours (1560 total hours) of work! Not counting your days off, you’re working 37.5 hours/week, and even if we do count those, it’s still an average of 30 hours/week over the course of a year!
  • And I’ll be damned if you’re going to take that day off! Your boss is a jackass.

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Blingee that has sparkles over the word "math" with a running unicorn and a caption that says "oh snap!"

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[E] Hillary

Hillary is a giant nerd and former Mathlete. She once read large swaths of "Why Evolution is True" and a geology book aloud to her infant daughter, in the hopes of a) instilling a love of science in her from a very young age and b) boring her to sleep. After escaping the wilds of Waco, Texas and spending the next decade in NYC, she currently lives in upstate New York, where she misses being able to get decent pizza and Chinese takeout delivered to her house. She lost on Jeopardy.

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