Horizon Distance Calculator
Use this tool to estimate how far away the horizon is from your eye height above a smooth surface (such as the ocean), and optionally compute maximum line-of-sight distance to another object.
Results are idealized estimates for a spherical planet and clear viewing conditions. Terrain, weather, and haze can reduce visible distance.
What this “how far is the horizon” calculator tells you
The horizon is the apparent line where the sky meets the surface. If you stand on a beach, it can look flat and endless, but geometry limits how far you can see. This calculator estimates that distance based on your height above the surface. The higher you are, the farther your horizon.
It reports two useful values:
- Line distance: straight-line distance from your eye to the tangent point on the surface.
- Surface distance: distance measured along the curve of the surface (arc length).
If you enter a target object height, the tool also estimates the maximum line-of-sight distance between both elevations (for example, person to lighthouse, ship to coastline, drone to tower).
The horizon distance formula (exact and practical)
Exact geometry
For a sphere, with radius R and observer height h:
For Earth, using R ≈ 6371 km, both values are very close at everyday heights.
Quick approximations
When height is small compared with Earth’s radius, these shortcuts are popular:
- d (km) ≈ 3.57 × √h, where h is in meters
- d (miles) ≈ 1.22 × √h, where h is in feet
These are handy mental math versions of the same geometry.
Why atmospheric refraction matters
Light bends slightly in Earth’s atmosphere, especially over water. A common first-order model is to increase Earth’s effective radius by a factor of 7/6. In practice, this increases calculated horizon distance by roughly 8% compared with pure geometry.
Refraction is not constant. Temperature gradients and weather conditions can make the true visible horizon shorter or longer than standard assumptions.
Example horizon distances (Earth, no target height)
| Observer height | Approx horizon (no refraction) | Approx horizon (standard refraction) |
|---|---|---|
| 1.7 m (average eye level) | ~4.7 km (2.9 mi) | ~5.1 km (3.2 mi) |
| 10 m (small cliff / deck) | ~11.3 km (7.0 mi) | ~12.2 km (7.6 mi) |
| 100 m (tall hill) | ~35.7 km (22.2 mi) | ~38.6 km (24.0 mi) |
| 1,000 m (mountain viewpoint) | ~112.9 km (70.1 mi) | ~122 km (75.8 mi) |
Two-height line-of-sight distance
If both observer and target have height above the surface, each has its own horizon distance. A common approximation for maximum visibility between them is:
That’s why tall ships can be seen from farther away, and why elevated radar or communication towers dramatically increase range.
How to use this calculator correctly
- Use eye height, not total body height, for a person.
- Use a realistic height above local surface (sea level is not always your local reference).
- For marine use, leave refraction enabled for a practical first estimate.
- For scientific geometry comparisons, disable refraction.
- Remember: obstacles, haze, waves, and curvature all interact in real viewing conditions.
FAQ
Is this a curvature-of-Earth calculator too?
In effect, yes. Horizon distance is a direct consequence of spherical geometry. The farther your elevation, the farther the tangent point where your line of sight meets the surface.
Why can’t I always see as far as the calculator says?
The model assumes a smooth surface and clear air. Real-world limits include hills, buildings, vegetation, aerosols, humidity, and optical conditions near the surface.
Can I use this for other planets?
Yes. Replace Earth’s radius with another planet’s mean radius. For example, Mars is about 3389.5 km. Keep in mind atmosphere and terrain differ greatly by planet.
Bottom line
This horizon distance calculator gives a fast, practical estimate for line-of-sight range from height. It is useful for sailing, photography planning, drone scouting, astronomy sites, and general curiosity. Enter your numbers above and instantly get horizon distance in kilometers, miles, and nautical miles.