A lovely round planet we call home

Is The Earth Round?

Good news: you can settle this yourself with binoculars, a distant building, and 4th-grade math. No YouTube rabbit holes required. If the Earth is round, the math will check out. If it's flat, I'll eat my telescope.

The DIY "Prove It Yourself" Challenge Grab your binoculars. Pick a tall building far away. Drive toward it and take notes.
Then come back here and let the math do the talking.
(No conspiracy theories were harmed in the making of this calculator.)

Here's the plan. Pick a building you can see off in the distance -- at least 3 miles away works best.

  1. Check Google Maps for the distance (or pace it out if you're feeling adventurous).
  2. Look through your binoculars or telescope. Note the lowest thing you can see on the building.
  3. Drive a bit closer. Take another look. Write it down again.
  4. Keep going until you're at the building, collecting data like a big-brain road-tripper.

Plug your numbers in below and let's see what the Earth has to say for itself!

You (hero) sneaky curve Building hidden! distance (miles)
0
people have used this calculator to do their own science
(number may be completely made up for dramatic effect)
Cheat Sheet - What's Hiding Behind the Curve

How much of a distant object is playing peekaboo behind Earth's curve, assuming your eyes are 5.5 ft off the ground. Handy if you're eyeballing your distance.

DistanceHidden
DistanceHidden
About You
(standing on tippy-toes counts)
Your Field Notes
# Distance to building (mi) Hidden height (ft)
The Verdict Is In
Your Calculated Earth Radius
--
Actual Earth Radius
3,959mi
6,371 km (give or take a mountain)
How Close You Got
--
Curve Per Mile
--
The Big-Brain Details (Per-Pair Breakdown)
Stops Radius (mi) Error Vibe
OK but how does this actually work? (click for the galaxy-brain details)

When you stare at a distant building, the Earth curves away beneath your line of sight like a very, very gentle hill. The bottom of the building gets hidden behind this curve. How much gets hidden depends on three things:

1. How far away the building is
2. How tall you are (every inch counts!)
3. How big around the Earth is (the whole point of this)

hidden = sqrt(d^2 + R^2) - R - h_eye + (d^2)/(2R)

Simplified: hidden ~ (d^2) / (2R) - h_eye_drop

The clever bit -- using two observation points cancels out errors:
R = (d1^2 - d2^2) / (2 * (h1 - h2))

By measuring from multiple spots and comparing notes, we can solve for R (the radius of the whole dang planet). More measurements = less error, because math is cool like that.

Scientists say the mean radius is 3,959 miles (6,371 km). With careful measurements, you can get within a few percent with nothing but your eyeballs and some basic arithmetic. Take THAT, ancient Greeks. Actually, they figured this out too. Respect.