Horizon Distance Calculator
Quick answer: Enter a height, or click a point on the map, to get the distance to the visible horizon. Both the geometric and the refraction-corrected figures are shown.
How to use horizon distance calculator
- Enter the observer’s eye height in metres; a standing-person example is 1.7 m.
- Read the geometric horizon and the separate approximate refraction-adjusted distance.
- Use the map only for location context: the spherical height calculation does not need a map click.
Worked example
- Input
- Eye height 1.7 m above a flat sea surface
- Expected result
- Geometric horizon about 4.65 km (2.89 miles); with the simple refraction allowance, about 5.03 km.
The distance grows with the square root of height. Four times the eye height gives roughly twice the horizon distance.
Calculation method and accuracy
The geometric tangent distance is √(2Rh + h²), with Earth radius R = 6,371,008.8 m and height h in metres. The refraction illustration adds 8%; it is a rough optical model, not a current atmospheric measurement. Heights refer to the observer above the surface being considered.
Common mistakes and edge cases
- Elevation above sea level is not always your height above the visible surrounding surface.
- Mountains, buildings, haze and clouds can obstruct visibility much sooner.
- A distant elevated object can be visible beyond your own sea-level horizon. Add the two horizon distances for a first estimate of mutual visibility.
Sources and verification
Reviewed by GeoDataViewer · . Examples are rounded; the interactive result uses your selected inputs.
How the distance is calculated
The geometric horizon distance comes from Pythagoras: if the Earth has radius R and your eye is height h above the surface, the horizon is at the distance where your line of sight is tangent to the Earth. That gives d = √(2Rh + h²).
At 100 metres up, that is about 35.7 km. At the top of Everest, nearly 340 km. From a commercial aircraft at 11 km, roughly 375 km.
Refraction makes the real horizon further
Light bends as it passes through the atmosphere, which curves the apparent line of sight downward and extends the visible horizon by roughly 8%. The commonly used approximation is d ≈ 3.57√h with h in metres and d in kilometres, which already includes the refraction correction.
This tool shows both, so you can see which convention a figure you are comparing against is using.
Why the answer assumes a clear line of sight
The horizon distance is a geometric limit, not a visibility forecast. Haze, terrain, and buildings usually cut the visible distance well below it. Conversely, from a high point you can sometimes see a distant peak that is itself above the horizon, even though the land between is hidden.
Limitations to keep in mind
This is the geometric horizon for a smooth sphere, optionally corrected for standard atmospheric refraction. Real terrain, buildings, and abnormal atmospheric conditions will change what you can actually see.
Related tools
- Crow-flies distanceStraight-line distance between any two points.
- Bearing calculatorCompass bearing from one point to another.
- Halfway pointThe great-circle midpoint between two places.
- Antipode finderThe point on the exact opposite side of the globe.
- Geographic centreThe centre of several points you pick.
Frequently asked questions
- How far is the horizon?
- It depends entirely on your height. At eye level, about 1.7 m, it is roughly 4.7 km. At 10 m it is about 11 km, and at 100 m about 36 km.
- What is the formula?
- d = √(2Rh + h²), where R is the Earth's radius and h is your height above the surface. The simpler 3.57√h approximation is accurate enough below about 100 km.
- Does atmospheric refraction matter?
- It extends the visible horizon by about 8%, which is why the common shortcut already includes it. This tool shows both figures so you can match whatever convention you are working in.
- Why is the horizon at sea always the same distance?
- Because it depends only on your height above the water. Standing on a deck at a fixed eye height, the horizon is at a fixed distance.
- Can I see further from a mountain?
- Yes, and dramatically. Height grows the horizon distance with its square root, so going from 2 m to 200 m multiplies it by ten.
- Does this account for hills in the way?
- No. The calculation assumes an unobstructed line of sight over a smooth sphere. Terrain almost always reduces the real distance.
- Why can I sometimes see distant mountains that should be below the horizon?
- Because they are tall enough to poke above your horizon line. The tool measures to the horizon itself, not to specific objects beyond it.
- How far can you see from a plane?
- From 11 km up, about 375 km geometrically, or around 405 km with refraction. In practice haze usually limits it far more.
- What is the difference between horizon distance and line-of-sight distance?
- Horizon distance is to the curve of the Earth. Line-of-sight distance is to a specific target, which may be nearer because of terrain or further because the target is elevated.
- Does the height of the observer or the target matter?
- Both. The full line-of-sight formula adds the two horizon distances, so a tall observer and a tall target can see each other over a longer span than either could see to the horizon alone.