Line of Sight Distance Calculator
The curved Earth limits how far two elevated points can see each other. The line of sight distance is the sum of each point's distance to the geometric horizon, which grows with the square root of height. This calculator takes two heights above the surface in meters and an effective Earth radius factor (1 for visual line of sight, about 1.333 for radio paths that bend with atmospheric refraction) and returns the maximum clear-path distance in kilometers and miles. It assumes a smooth sphere with no terrain or obstacles.
Line of sight formula
Effective radius Re = k * 6,371,000 m
Horizon from height h = sqrt(2 * Re * h)
Line of sight = sqrt(2*Re*h1) + sqrt(2*Re*h2)
k = 1 for visual, about 1.333 for radio refraction
1 km = 0.621371 miles
Horizon distance scales with the square root of height, so tall sites reach much farther. The 4/3 effective radius approximates standard atmospheric refraction for radio links.
Line of sight context
- Horizon distance grows as the square root of antenna or observer height.
- Use k = 1 for optical sight lines and about 1.333 for typical radio paths.
- Raising both endpoints multiplies the achievable link distance.
- The model assumes a smooth sphere with no hills, buildings, or trees.
- Real radio links also need Fresnel-zone clearance, not just a clear sight line.
Line of sight: frequently asked questions
What is the line of sight distance?
It is the maximum distance over the curved Earth at which two points, each at some height above the surface, can see each other without the bulge of the Earth blocking the path. It is the sum of each point's distance to the geometric horizon.
How is it calculated?
The distance from a height h to the horizon over a sphere is the square root of (2 times the effective Earth radius times h). The line of sight distance between two heights is the sum of the two horizon distances. With the Earth radius in meters, the result is in meters.
What is the effective Earth radius factor?
For optical line of sight the factor is 1 (true Earth radius). For radio propagation, atmospheric refraction bends signals around the curve, so engineers use an effective radius of about 4/3 (1.333) times the true radius. Enter 1 for visual line of sight or 1.333 for typical radio paths.
Why does antenna height matter so much?
Horizon distance grows with the square root of height, so doubling height increases reach by about 41 percent. Raising both endpoints, for example a tall tower talking to a tall tower, multiplies the achievable link distance, which is why broadcast and microwave sites are placed high.
Does this account for terrain and obstacles?
No. It assumes a smooth spherical Earth with no hills, buildings, or vegetation in the path. Real links must also clear terrain and maintain Fresnel-zone clearance. Treat this as the theoretical maximum for a clear, smooth path.
Official sources
- U.S. Geological Survey: U.S. Geological Survey.
- NIST: Fundamental physical constants and units.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.