Distance to Horizon Calculator
Enter your eye height and (optionally) a target height to estimate line-of-sight distance on Earth.
Assumes a spherical Earth and clear line of sight. Terrain, weather, and local conditions can reduce visibility.
What this horizon distance calculator tells you
The horizon is the farthest point you can see before Earth’s curvature blocks your view. This distance grows as your viewing height increases. If you also know the height of a distant object (like a ship mast, radio tower, or mountain), you can estimate the maximum distance at which it could still be visible.
Quick idea
- Higher eye level = farther horizon.
- Higher distant object = visible from farther away.
- Atmospheric refraction usually extends the visible distance slightly.
The formula used
For a viewer at height h above Earth’s surface and Earth radius R, the geometric horizon distance is:
For small heights relative to Earth’s radius, this is often approximated as:
When both observer and target heights are considered, maximum line-of-sight distance is:
Why refraction matters
Light rays bend slightly in the atmosphere, which effectively increases Earth’s radius for visibility calculations. A common engineering approximation is using Reffective = (7/6)R. That’s what the checkbox in this tool enables.
Example scenarios
Standing on a beach
With eye height around 1.7 m, your horizon is roughly a few kilometers away. If a ship’s bridge is much higher, it can appear before the hull becomes visible.
From a lighthouse or hilltop
At 30 m height, the horizon jumps significantly compared with sea level. Elevated viewpoints are useful for marine navigation and lookout planning.
Drone and radio planning
This same geometry is used in quick line-of-sight estimates for drones, surveillance, and RF links. It does not replace full terrain/path analysis, but it gives a strong first approximation.
How to use this tool effectively
- Use eye height above local surface for observer height.
- Use visible top height for a target (mast, tower, etc.).
- Enable refraction for standard outdoor conditions.
- For strict geometric results (no atmosphere), uncheck refraction.
Common limitations
- Ignores hills, buildings, trees, and waves.
- Assumes standard atmosphere when refraction is enabled.
- Does not model haze, fog, or contrast limits of human vision.
- Uses mean Earth radius, not local ellipsoid corrections.
FAQ
Is this accurate for everyday use?
Yes, for quick estimates and education. For mission-critical surveying or long-range optics, use advanced geodetic models.
Do I enter height above sea level or above ground?
Enter height above your local surface where you observe from. For marine use, this is usually above sea level at that location.
Why is there a target height field?
Because two elevated points can see each other farther than one elevated point and one ground-level point.
Can this be used for Earth curvature checks?
Yes. It directly quantifies how curvature limits line-of-sight distance.