Horizon Distance Calculator
Enter your eye height and (optionally) the height of the object you are trying to see. The tool calculates the geometric distance to the horizon and the maximum line-of-sight distance.
What this horizon calculator tells you
This calculator answers a practical question: how far can you see on the horizon from a given height. It is useful for hikers, sailors, photographers, drone pilots, beachgoers, and anyone curious about line-of-sight distance on a curved Earth.
The tool gives you two key outputs:
- Distance to your horizon (from your eye height only).
- Maximum line-of-sight distance to a target when the target has its own height (for example, a lighthouse, mountain, or ship mast).
Quick rule of thumb
If you just need a fast estimate, these are commonly used approximations:
Distance to horizon (miles) ≈ 1.23 × √(height in feet)
Those are for geometric horizon distance and are very close to what the calculator computes.
How the math works
1) Horizon distance from one height
The calculator uses Earth geometry with radius R and observer height h:
Where d is distance to horizon. For small heights, this simplifies to √(2Rh), which is why the square-root rule appears in most shortcuts.
2) Seeing another object above the horizon
If a target has height h₂, it also has its own horizon distance. The total potential line-of-sight distance is:
This explains why tall towers and mountain peaks are visible from much farther away than low objects.
About atmospheric refraction
Light bends slightly in the atmosphere, letting you see a bit farther than pure geometry predicts. A common engineering approximation is to use an “effective Earth radius” of about 7/6 of actual radius.
- Refraction off: strict geometric horizon.
- Refraction on: typical real-world viewing condition estimate.
Conditions such as temperature inversions, haze, humidity, and pressure gradients can still move real visibility above or below the estimate.
Example scenarios
Standing person at the beach
Eye height around 1.7 m gives a horizon distance of only a few kilometers. This is why distant boats “disappear from the bottom up.”
Cliff viewpoint
At 100 m elevation, your horizon is much farther than at sea level. Elevation increases visibility fast, but with diminishing returns due to the square-root relationship.
Ship-to-ship visibility
If both observers are elevated (for example, bridge decks and masts), their horizon distances add. This can significantly extend mutual detection range.
FAQ
Is this the same as weather visibility?
No. This tool calculates geometric line-of-sight limit due to Earth curvature. Fog, haze, rain, and pollution can reduce practical visibility long before the geometric horizon.
Does this prove Earth curvature?
The horizon-distance relationship follows spherical geometry and matches many everyday observations: objects vanish hull-first, and elevated viewpoints see farther.
Can I use this for drones or photography planning?
Yes. It is useful for planning shots, lookout points, and approximate visibility. For mission-critical work, use local terrain/DEM data and atmospheric models in addition to this estimate.
Final note
A horizon calculator is a simple but powerful way to understand perspective, Earth curvature, and why height matters so much for visibility. Try a few different heights and target values above to build intuition quickly.