How to Think About the Size of the Earth

You’ve no doubt noticed that the Earth is a big place, but do you have a good feeling for exactly how big? If you’re like most people, you probably don’t have an intuition for this kind of thing … because we humans just aren’t very good at thinking about huge numbers and the huge objects described by them. But that doesn’t mean we can’t develop this kind of intuition—we absolutely can, but it takes a bit of thinking. Which is exactly what we’re going to do today.

By the way, when I talk about knowing how big the Earth is, I’m not talking about being able to recite its radius or circumference in some arbitrary human units like miles or kilometers—because deep down that really doesn’t help you understand its size, right? I’m talking about developing intuition about its size—the kind of thing you can only obtain when you figure out a way to think about things in terms that you can personally identify with.

So let’s get to it … let’s start developing our intuition for just how big the Earth really is.

How Big Is the Earth’s Radius?

Since our goal for today is ultimately to figure out how to think about the size of the Earth, we’d best begin with its size. So here goes: the radius of the Earth is about 6,370 kilometers or 3,960 miles. And we’re done! Except as I mentioned earlier if you’re like me, you don’t actually know how to think about these numbers and what they mean. So instead of worrying about the numbers, I want you to instead think about something that you’re more familiar with that’s roughly this size.

The radius of the Earth is about 1.5 times the distance across the United States.

Here’s how I think about this. At various points in my life, I’ve lived in both Los Angeles and New York … and I’ve driven back and forth between the two sides of the United States several times. As such, I have a good intuitive feel for just how far this is. Namely, it’s really far—it takes roughly four very long days in the car to complete the journey. I’ve also spent a fair bit of time staring at maps and globes, so I have a decent big-picture idea about how the distance across the US compares to the total size of the Earth.

And that’s all I really need to understand the size of the giant ball of a planet that we inhabit. Because it turns out that the distance from New York City to Los Angeles is around 4,000 kilometers or 2,500 miles. Which means that the radius of the Earth is about 3,960/2,500 or roughly 1.5 times the distance across the United States. For me, this is a great way to think about the size of the Earth. I just imagine getting in my car and beginning a journey across the country … except in this case, I’m not traveling east from Los Angeles, I’m traveling directly down towards the center of the Earth. If I could somehow do this, it’d take about six long days of driving to complete the journey!

How Big Is the Earth’s Circumference?

Once you know that the radius of Earth is roughly 1.5 times the distance across the United States, you can use this new point of reference to think about the size of the Earth in another way. In particular, if you remember the basics of the geometry of circles, you’ll know that the circumference of a circle (that’s the distance around it) is equal to 2π times the radius of the circle. This geometric relationship is true for any circle—including the circle formed as part of what’s called a “great circle” around the Earth. (Well, if we’re being super-precise, the Earth isn’t a perfect sphere … so this geometry isn’t exactly exact—but it’s close enough.)

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The distance around the equator is around 10 times larger than the distance across the US.

On the Earth, every line of longitude (those are the lines running around the Earth through its North and South Poles) is a great circle, and so is its equator. So let’s use all of this information to think about the size of the Earth in terms of its circumference—which, as we’ve just seen, is the same as the distance around its equator. We discovered earlier that the radius of the Earth is roughly 1.5 times the distance across the US. So how does this distance across the US compare to the distance around the entire planet? Well, geometry tells us that the circumference of a circle is 2π times the circle’s radius. Since π is approximately equal to 3.1, this says that the circumference of a circle is a little more than 6 times longer than its radius.

So in the case of the Earth and our newfound ways of thinking about its size, we’ve just discovered that the distance around the equator is around 1.5 x 6 or roughly 10 times larger than the distance across the US. And if you think about how the US appears on a globe (or better yet take a look at a globe if you have one handy), you’ll realize that this makes perfect sense—the US really does span about 1/10 of the way around the entire planet.

How Big Is the Moon Compared to Earth?

Now that we have an intuitive sense for the size of the Earth, let’s quickly compare that to the size of the Moon. The diameter of our celestial companion is about 1/4 the diameter of the Earth … which is actually a lot bigger than most people think!

This means that the radius of the Moon is also 1/4 the radius of the Earth. Or, thinking about this in our more intuitive way, the radius of the Moon is a little less than half the distance between New York and Los Angeles—which, for those of you familiar with the west coast of the US, is about the distance between Los Angeles and Portland, OR. In terms of circumference, the distance around the Moon is therefore a bit more than twice the distance across the United States.

The Moon is pretty big, but the Earth is definitely a lot bigger. And as we’ve seen, all that you really need to develop a feel for this is a bit of geometrical knowledge and a willingness to take the time to think about things in a way that you can more closely identify with.

Wrap Up

Okay, that's all the math we have time for today.

For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. Also, remember to become a fan of The Math Dude on Facebook and to follow me on Twitter.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Earth and Earth-Moon images from Shutterstock.