Square Footage

This one’s mine!

So I was conversing with a fellow I know, and the right side of my brain asked the left side, “So just how much square footage per person is there these days?” We both agreed that seemed like an interesting question (given all the people running around these days), so we looked around for a body to help us research the answer.

We just happened to find one handy, so off we all went to the virtual library and math lab.  Unfortunately our math consultant was a Communications Arts major and made a small error thinking square kilometers to square miles was the same as kilometers to miles. Fortunately everyone involved obsessively double-checks their work, so we caught the error in time.

Pity, though. The original answer would have been fun to write about.

But the actual answer is pretty interesting, too!

We started with the total world population, as provided by World-o-Meters. The number increases by the minute, so we rounded up:

Yikes, we passed seven billion! Seems like just yesterday it was six.

Our research department found discovering the available earth land surface more challenging (especially with the math errors and the distraction of a baseball game).  Like the population, it’s a number that changes depending mostly on exactly what you consider land (ice shelves, for example). Unlike population, which just keeps increasing, land surface area is just tricky to pin down.

[Sea level also plays a role, but the coast line doesn't change that much in the short-term. However... if all the ice in Greenland were to melt — making Greenland more like its namesake and less like its little neighbor's namesake (who ironically also has it backwards)] — the sea level would rise about 22 feet. That may not sound like much, but say goodbye to Manhattan, much of Florida, and a lot of other nice coastal area.]

In any event, after considerable debate (and dinner) the research department (all except for two parts of the mind: one wanted to watch TV, the other voted for a nap) decided on a figure:

Or for us metrics-challenged folks:

Which is a whopping:

(Wouldn’t you like to see the Real Estate ad with that figure?)

Carry the four…

From there it seemed like a simple bit of math: Divide the land surface area by the number of people, and the result is how much square area each person has.

That’s assuming we distributed all the Earth’s population evenly across all land area. (You can probably see the problem already, but I’ll get to that later.)

((And no, the problem isn’t the difficulty in convincing all those people to spread out. That’s what the cattle prods are for.))

The answer turns out to be:

Jus’ chillin’ and enjoyin’ my 357 foot² lot!

So we each get over 200,000 square feet of land to call our own! If we take “square footage” seriously, that forms a square patch just a hair under 473 feet on all sides. (Or you can have a plot one foot wide and 472+ feet long.)

As a square, that’s about the size of a (rather large) baseball field. For reference, Target Field in Minnesota is 328 feet by 339 feet, and some of the outfield is cut off by the fence (it’s only 404 feet to the center field fence, but the actual diagonal to the far corner would be 470-ish).

That’s a goodly patch of land! The only thing is, for some of us, it’s located on Mount Everest, or the middle of the desert or deep in the Amazon jungle. (That’s the problem alluded to above!) It’s going to be difficult for them to build a baseball field when lack of water or oxygen is a concern!

We can make those poor souls more comfortable by forfeiting the deserts and mountains. (But who wouldn’t want a baseball field in the Amazon jungle!) According the University of Texas, “33% is desert and about 24% is mountainous.” Subtracting that 57% gives us:

After doing the math again, we find out that now we all get:

So, to accommodate everyone more comfortably, we’ll have to close ranks a bit and settle for just over 125,000 square feet. That still makes a square patch 357 feet on a side (or about 108.7 meters), and that’s still (very large) baseball field-sized!

Steam rooms to the left, bowling alley on the right!

Of course, these are all ramblers. If we go vertical, we can increase our personal footage. (I’m thinking Olympic-size pool and steam rooms in the basement (maybe a bowling alley) and a sprawling space observatory and dog park on the roof!)

You might be wondering about that math error. Or if you’re more math astute, laughing about it.  Turns out the standard conversion of kilometers to miles isn’t directly useable when it comes to square kilometers and miles.  A little thought shows why:

Imagine you have a small plot one kilometer square. Each side is 1 km, which means each side is 0.621371 miles. If you naively convert 1 square km to square miles (using the same factor), you’d get the answer 0.62+ square miles. But consider the formula to calculate square whatevers: multiply one side by the other. If we multiply 1 km side by the other 1 km side, sure enough, we get 1 square km.

But here’s the trick: if we multiply 0.621371 by itself, we get 0.38610, and that is the correct answer!

When I did the square footage calculation the wrong way, I came up with that we all got a patch about 70 feet on a side.  That’s smaller than a baseball diamond (which is 90 feet on a side).  I found that answer very surprising, since I thought I’d heard much larger answers in the past. Surprising answers demand a closer look and double-checking.

And if I’ve learned one thing in my years as a computer programmer (actually I’ve learned quite a few things), it’s that when the system or answer seems way out of whack, it’s almost always an error on my part.

But just for grins, I did take a look at how much the situation has changed since we had six billion.  Back then (October 1999), we all had:

Which amounted to a patch about 390.7 feet on a side (119 meters).

Back at the five billion mark (July 1987 — 26 years ago):

And that gave us very nearly 428 side feet on our lots (130.3 meters). That’s noticeably more elbow room (although it’s less than we’d have today if we used all available land surface area). But still, at that size we could include the entire ballpark, not just the field (which gives us access to the concession stands!).

Let’s make one more jump, back to the three billion mark in 1960:

Back in those days we had vast estates over 552 feet on each side (168.2 meters)! It was a much longer walk to go borrow a cup of sugar. On the other hand, we had the parking lot in addition to the ballpark.

All in all, it’s getting more crowded, obviously, but even on our 357-foot lots there’s a fair bit of space. We’ll all have to chip in for roads and public buildings, and no doubt some will join together to farm.

(We’ll have to make sure the farmer-types get the farm land!)  If we all give up half our square footage, we’d still be able to have lots over 250 feet on a side.

One more thing: I’m calling dibs on Target Field!

[By the way, hello, Communication Arts major, so you might want to check the math. Sure, I was a computer programmer for three decades, but we only used ones and zeros, so — again — check the math! You always should anyway.]