Horizon distance calculator

The presets, worked

How to use it

1. Type your eye height in meters in Eye height, or press a preset: Beach (1.7 m), Lighthouse (30 m), Everest (8,849 m), or Airliner (10,668 m).
2. The card updates at once with the horizon distance in kilometers and miles, the dip angle in degrees, and the refraction allowance used.
3. Click the map to move the observer. A circle shows how far the horizon reaches in every direction from that point.
4. For a height in feet, divide by 3.28084 to get meters first.

The formula

Your line of sight to the horizon touches the Earth at a right angle to the radius. With eye height h and Earth radius R, the distance is √(h · (2R + h)). For everyday heights that is close to √(2Rh), about 3.57 · √h kilometers with h in meters.

The dip angle is how far below horizontal you look to see the horizon, atan(d / R). It is small: well under a tenth of a degree at beach height. The horizon guide derives both.

The refraction allowance

Air is denser near the ground, which bends light slightly downward and lets you see past the geometric horizon. The tool multiplies the geometric distance by 1.0746 to allow for typical conditions. On any given day the real value varies with the temperature profile of the air, and over water it can differ a lot.

Seeing a distant object

The horizon distance tells you where the sea surface disappears. A tall object farther away can still show above it, because the object has its own horizon. The top of it is visible when your horizon distance plus its horizon distance exceeds the gap between you. Enter the object's height to get its horizon, then add the two numbers.

On land, hills and buildings usually block the view first. Check the ground between two points with the elevation profile.