The view from Emery Peak, the highest
point in Big Bend National Park
(elev. 7825 ft.)

Most people have experienced looking from the top of a skyscraper, the peak of a hill, or the window of an airplane. Sometimes it seems you can see forever. While the actual distance you can see is dependent upon the weather, air quality, and local terrain, a little math can tell you the maximum distance you can see from a given height. You just need a right triangle and the radius of the Earth.

The diagram below shows a right triangle formed by the center of the Earth, your eyeball, and the farthest point you can see. We know the radius of the Earth is about 3,963 miles (or close to 21 million feet). If you know how far above the Earth your observation point stands, you know two measurements of the right triangle in the diagram. We can use the Pythagorean Theorem to calculate the third measure -- the distance you can see to the horizon. 6378.1 kilometers 3280.8399

r = radius of the Earth h = your height above the Earth d = distance you can see

Remember the Pythagorean Theorem says that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. We often write this theorem as:

Let's apply this formula to find the maximum distance one could see from Emery Peak, the highest point in Big Bend National Park at 7,825 feet above sea level.

This means the hypotenuse (longest side) of our right triangle is 21,000,000 + 7825 feet and one of the legs is 21,000,000 feet. We only need to calculate the length of the missing leg. The Pythagorean Theorem give us:

Here's the formula to calculate the maximum visible distance from a height of h feet: