Distance to Horizon Calculator

How it is calculated

The distance to the horizon is d (km) = 3.57 × √h, where h is the height of the eye above the surface in metres. The constant 3.57 comes from the geometry of a spherical Earth, d ≈ √(2Rh), with the Earth's radius built in. The kilometre result is converted to miles by multiplying by 0.621371. Both are rounded to two decimals. A height of 0 gives 0 and a negative height gives no result. Distance grows with the square root of height, so quadrupling the height only doubles the distance. The formula assumes a smooth sea-level surface and ignores atmospheric refraction, hills, waves and the height of the object you are looking at.

Common mistakes

• Entering the height in feet or centimetres. The field is in metres, so 6 ft should be typed as about 1.8 and 170 cm as 1.7.
• Expecting a linear relationship. Twice the height gives only about 41% more distance, not double.
• Reading the result as how far away a ship or building can be seen. It is the distance to the horizon for one eye only; a tall object is visible beyond it, and you add the horizon distance of the target's height.
• Using it for land with hills or mountains. The formula assumes a flat sea surface, so terrain in between blocks the view sooner.
• Counting on the exact value in real conditions. Atmospheric refraction usually bends light slightly and extends the visible range, which this tool does not model.