Can We Plant 20 Million Trees by 2020? The Math Says Yes

There’s a lot of power in a rough estimate. If you’re trying to figure out whether something is worth doing, you could really go deep into the weeds trying to capture all the costs and benefits. But here’s the thing: Usually you don’t need an exact answer in order to make the right decision.

For example, say you’re having a big party, a hundred people, and you want to make special decorated cupcakes. You do some quick, cocktail-napkin calculations and you guesstimate it would take 10 hours. Well, in reality it might be 9 hours, or it might be 11 hours—it doesn’t matter! It’s way too long.

That’s what I did in a recent post. I had wondered, if everyone on earth planted a tree—all 7.5 billion of us—how much carbon dioxide would it pull out of the air? My answer, based on some very rough assumptions, was that it could cut atmospheric CO2 levels by around 6 percent.

Some people disagreed with my result, and that’s fine. I’m sure it’s wrong. (For one thing, I modeled the carbon content of trees without branches.) But as a first cut, it tells us what we want to know: Planting trees can make a difference, even if it’s not in itself a solution to climate change. Besides, trees are beautiful.

Of course 7.5 billion was a fanciful number. And planting that many trees has its own complications, such as where the land is and how it was used before. But what about 20 million? Yes, we can do that, and for carbon reduction, every contribution matters. That’s the aim of the #TeamTrees project—to plant 20 million new trees. And you can help.

What’s that? You live in Manhattan? Or the Mojave? No sweat: The Arbor Day Foundation will plant a tree for every dollar you pledge—which, if you do some cupcake-type math, is a lot less than it would cost you in time and money. So the goal is to raise $20 million for reforestation by January 1, 2020. Go #TeamTrees!

How Much Land Would It Require?

Just for fun, how about a new estimation problem. How much land do you think it’ll take to plant 20 million new trees? What’s your intuition? Are we talking about a forest the size of Rhode Island? Even bigger?

I’m going to show how I’d come up with a ballpark estimate. And if you don’t agree with my answer, you can change the assumptions and make your own!

Step one is to estimate the area that one tree would require, then we’ll scale it up. Obviously the species matters, but I’m picturing a pine tree. You see these pretty close together in forests, with a separation of maybe just 3 meters. So from a bird’s-eye view, each tree is a circle with a radius of 1.5 meters.

I’ll assume the trees are in a square grid layout. Actually, there’s a whole field of math called “packing problems,” and if you worked it out, you’d find there is a better way to pack circles together to minimize the total space. But remember, this is an approximation. 80/20 rule. We’re looking for 80 percent of the truth with 20 percent of the effort.

Illustrator: Rhett Allain

With this arrangement, each tree takes up a square with sides equal to 2R, for an area of 4R2 square meters. Which means that altogether we need 20 million times 9 m2. Yes, you can do that in your head, but I put it in a Python script so you can change the assumptions and run your own estimation. Click on the pencil icon to edit the code, then hit the Play button to get the answer.

So I got 180 million square meters, or about 69 square miles. Not as big as I initially imagined—roughly the size of a state park? If it was a square area, it would be 8.3 miles on each side, for a total perimeter of 33 miles. You could walk all the way around these 20 million trees in a day! You’d need a lot of trail mix, but you could do it.

Want to solve a few more puzzles? Try these for extra credit.

  • How many years would it take one person to plant 20 million saplings?
  • Suppose you planted live oaks instead of pines. How would that affect the land requirement?
  • How much CO2 would a single tree remove from the atmosphere? You might start with my earlier post, but feel free to improve on it.
  • A small car gets 40 miles a gallon. Figure out how much CO2 is produced per gallon. Then convert the car’s gas mileage into miles per tree.
  • What if you could get the same carbon capture by planting one GIANT conifer with the same mass as 20 million trees? (Unrealistic? Hey, on the planet Kashyyyk, wroshyr trees can grow several kilometers tall. Any wookiee knows that.) Estimate the height of the tree and it’s diameter at the base. You can assume it has the same aspect ratio as a normal pine.

There’s two lessons here. First, as a practical matter, planting 20 million trees is doable. Second, a quick-and-dirty estimate often suffices to answer a question. You can always dig into the details and refine your analysis later. But as a first cut, keeping it simple means you won’t risk losing the forest for the trees.

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