In Lawrence Weinstein and John Adam’s book, Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin, we learn how to estimate the total length of all of the pickles consumed in the US each year, how many cells there are in a human body, how much electrical energy the US uses each year and much more. In celebration of Math Awareness Month and all the fun you can have with huge data sets, we’ll be posting problems from the book and the answers the following day. Join in the fun and post your guesses below in the comments field.

Remember — this is math that can be jotted down or performed in your head, so we’re not looking for exact answers.

# Question #1

#### If all the humans in the world were crammed together, how much area would we require? Compare this to the area of a large city, a state or small country, the US, Asia.

# Extra Credit

#### How much area would we need if we gave every family a house and a yard (i.e., a small plot of land)?

I know I’m the blog editor, but this looks fun. Here’s what I am thinking:

7 billion people on earth (remember, guessing and rounding up

2 square feet each (I’m going off the idea that we’re standing up shoulder to shoulder or somehow being squared to incorporate the width and depth of a rectangle box of 1 foot by two foot — thinking this allows for adults and children, big and small)

14,000,000,000 billion square feet (number of people times the square feet)

30,000,000 square feet in a square mile (I had to look this figure up…)

14,000 (I’m knocking off the extra zeroes to make this easier)

30

30 seems to go into 14,000 something like 466 times so I’m rounding up to:

500 square miles

New York City is about 470 square miles…

Can that possibly be right? It already seems like the population of NYC fills the space pretty well, could the rest of us fit in there too?

Roughly, if each person takes up 1.5 square feet on average standing up/crammed together (looking from above on each person’s head/shoulder space) and there are 7 billion people (give or take 6 or 7 million of us on 4/12/12), the space required would be 10.5 billion sq.ft. or about 1 billion sq. meters out of 120 trillion sq. meters of total land/water surface area. Figuring the house and yard would follow similar calculations, based on my calc methods.

US Census Population Clock

Comparing this total population to the total land area of a country, the 1 billion sq. meters becomes 1 million sq. kilometers which equals the approximate country size of Egypt. All the people in the world would fit into Egypt if packed extra tight. Or if allowing some room then it would be Mauritania, based on my assumption of 1.5 sq.ft per person (or .093 persons per sq. meter.) Or, we would all fit in the 29th and 30th area-sized countries in the world.

Country Land Areas per CIA World Factbook

So Jessica, I realized I made a mistake on my last calcs… using 7.5 billion people to figure my last submission instead of 7 billion. That error changes the country size to between Egypt and Tanzania, or Egypt with room to breath. Or between the 30th and 31st sized country. (Egypt is the 15th most populated country with 83 million citizens and Tanzania is the 30th in pop estimated 2012).

I also figured that since most of the world’s population is young (and dies relatively young) that the square space measures would be smaller than your 2 sq.ft. even allowing for the ever-super-sizing American girths.

Country Age Structures per CIA World Factbook

If you liked this exercise, Jessica, you might also like Google-a-Day

I came across your Twitter post on this topic/book… Thanks!

Solution is now posted: http://blog.press.princeton.edu/2012/04/17/solution-to-guesstimation-1/

Try Guesstimation #2: http://blog.press.princeton.edu/2012/04/17/guestimation-2/

Response…

We put every person (baby, bug men) in 1m.sq. Those who can’t stand have a chair fitting in 1m sq.

7000 000 000 persons * 1m.sq = 7000 km.sq or about 1/3rd of Vermont.