If Each of Us Planted a Tree, Would It Slow Global Warming?

Here are some self-evident truths: Humans need to produce less carbon dioxide—assuming we care a fig about our children’s well-being. But even that’s no longer enough. CO2 levels in the atmosphere have reached 400 parts per million, a huge increase over historical levels of around 300 ppm. The fact is, we also need to figure out how to remove some of the CO2 that’s already out there.

As a short-term solution, intrepid climate activist Greta Thunberg suggests we plant more trees. It’s a lovely idea. Who doesn’t like trees? While R&D labs struggle to come up with viable carbon-capture technologies, we already have this “magic machine,” as her video says, that “sucks carbon out of the air, cost very little, and builds itself.” And we don’t need to wait for craven politicians to get on board.

I really want to believe in this. What if every person on Earth took it upon themself to plant a tree. One treetop per child. Just how much carbon dioxide could we hope to scrub out of the atmosphere? Would it help reverse climate change? Let’s do the math!

Carbon Content of a Tree

I’m going to walk through a rough estimation. This is a good way to approach policy questions on a first cut; if the results are promising, you can always loop back and do a more sophisticated analysis.

So to start, let’s figure out how much carbon a single tree can hold. Imagine a generic tree. Since I live in Louisiana, I’m picturing a pine (though we have some awesome oak trees here too).

The pine is nice because it has a tractable shape—it’s basically just a long skinny cylinder (ignoring the branches). I’ll say it has a diameter (d ) of 1.5 meters and a height (h ) of 15 meters. I can just plug those values into the formula for the volume of a cylinder to get the amount of wood my tree contains.

Illustration: Rhett Allain

This gives me 106 cubic meters of wood. To convert this to mass, I’m going to assume a wood density (ρ) of 500 kilograms per cubic meter, which is half the density of water. The mass of my generic tree would then be:

Illustration: Rhett Allain

That works out to 53,000 kilograms per tree. But how much of that is carbon? Trees are made of many different elements, like hydrogen and nitrogen, but let’s say it’s about half carbon. At least that’s an estimate that agrees with Wikipedia. So the mass of carbon would be 0.5 times the mass of the tree, or 26,500 kg. Simple!

Counting Up the Atoms

So far so good. But to talk about atmospheric concentration, what we really need to know is the number of carbon dioxide molecules eliminated. Since each CO2 molecule contains one carbon atom, I need to convert the carbon mass of a tree to numbers. This is where Avogadro’s number comes into play, with a value of around 6.022 x 1023 particles per mole. And one mole of carbon has a mass of about 12 grams. That gives us the number of carbon atoms (n) per tree:

Illustration: Rhett Allain

Then, since everybody plants a tree, and assuming they’re all the same, the total amount of captured carbon atoms (N) would just be that number times 7.5 billion, the population of Earth.

We’re not done yet. We still need to find out how this changes the total concentration of CO2 in the air. For that, we need to estimate the total mass of Earth’s atmosphere …. well, that’s kind of daunting. What do physicists do in such situations? We Google it. I get a value of 5 x 1018 kilograms (from Wikipedia again).

So, to find the concentration in ppm, I need the molar mass of air. Air is 99 percent nitrogen and oxygen; a weighted average of their masses gives an air molar mass of 28.97 grams per mole. With that, I can calculate the number of air molecules. This uses the same formula as above for n, so I just built it into my computation code.

The Grand Result

OK, let’s crank this sucker out! I’m attaching the code here, so if you want to change my assumptions—perhaps, in keeping with the tropical theme of Earth’s future, you’re envisioning palm trees instead of pine trees— you can click the pencil icon to edit it. Click Play to run the calculation.

Damn. That sucks. Even with 7.5 BILLION trees, it makes only a tiny dent in the carbon dioxide level. Yes, we made a lot of assumptions, and some of them are obviously wrong—but they’re not crazy-wrong. For example, we simplified by saying the trees are all the same. But allowing them to be different wouldn’t change the result if our generic tree is a good middle-of-the-pack average. The real question is whether our model is biased in one direction or the other.

One obvious bias is that we assumed away branches. (I’m trying to picture a poor village smithy standing under a non-spreading chestnut tree …) But how much more carbon would we trap with branches? Twenty percent? Even if it doubles the reduction, the atmospheric concentration of CO2 still rounds off to 400 ppm.

How about one more quick estimation. If everyone planted a tree, how much land would that require? Let’s say they’re planted in a square grid, 5 meters apart, so that each tree takes up an area of 25 square meters. With 7.5 billion trees, that requires 1.8 x 1011 square meters of land, or 72,000 square miles. That’s roughly the size of North Dakota.

That’s not too bad. I think we could do that. And with all due respect, North Dakota could use some more trees. Oh, for comparison, the Amazon rain forest has an area of 2.1 million square miles. Please don’t burn it down.

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