Horizon
Approximation

If the observer is close to the surface of the Earth, then it is valid to disregard h in the term (2 R + h), and the formula becomes-

Using kilometres for d and R, and metres for h, and taking the radius of the Earth as 6371 km, the distance to the horizon is

Using imperial units, with d and R in statute miles (as commonly used on land), and h in feet, the distance to the horizon is

If d is in nautical miles, and h in feet, the constant factor is about 1.06, which is close enough to 1 that it is often ignored, giving:

These formulas may be used when h is much smaller than the radius of the Earth (6371 km or 3959 mi), including all views from any mountaintops, airplanes, or high-altitude balloons. With the constants as given, both the metric and imperial formulas are precise to within 1% (see the next section for how to obtain greater precision).If h is significant with respect to R, as with most satellites, then the approximation is no longer valid, and the exact formula is required.
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