The actual distance you’ll travel to get to the horizon will be longer because of surface curvature and (on land) irregularities. Proceed to the next method below for a more accurate (but complicated) formula.
By knowing the radius of the Earth and measuring your height of eye and local elevation, that leaves only the distance between your eyes and the horizon as unknown. Since the sides of the triangle that meet at the horizon actually form a right angle, we can use the Pythagorean theorem (good old a2 + b2 = c2) as the basis for this calculation, where:• a = R (the radius of the Earth)• b = the distance to the horizon, unknown• c = h (your height of eye) + R
d = R * arccos(R/(R + h)), where• d = distance to horizon• R = radius of the Earth• h = height of eye
The atmosphere bends (refracts) light that is traveling horizontally. What this usually means is that a ray of light is able to slightly follow the curvature of the earth, so that the optical horizon is a bit further away than the geometric horizon. Unfortunately the refraction due to the atmosphere is neither constant nor predictable, as it depends on the change of temperature with height. There is therefore no simple way to add a correction to the formula for the geometric horizon, though one may achieve an “average” correction by assuming a radius for the earth that is a bit greater than the true radius.
