Advanced Line of Sight Distance Calculator

Line of sight distance calculator

Unit system

Observer height above surface

Use meters for metric or feet for imperial.

Target height above surface

The second object height affects the shared horizon.

Earth radius

Default value is 6371 km.

Refraction mode

Custom refraction coefficient

Used only when custom mode is selected.

Required clearance

Subtracts a safety margin from each height.

Graph maximum target height

Graph x-axis limit in current height units.

Graph sample steps

More steps produce smoother plots.

Plotly graph

The chart shows how total line of sight distance changes when target height varies while observer height, curvature, and refraction remain fixed.

Example data table

Case	Observer Height	Target Height	Refraction Mode	Approx LOS Distance
Coastal lookout	30 m	10 m	Standard optical	31.05 km
Radio tower pair	60 m	60 m	Standard radio	62.25 km
Drone to rooftop	120 m	25 m	None	52.98 km
Hilltop observer	250 m	40 m	Custom k = 0.18	74.72 km

Formula used

1) Effective Earth radius with refraction

R_eff = R / (1 - k)

2) Horizon distance from one height

d = √(2R_effh + h²)

3) Combined line of sight distance

d_total = d_observer + d_target

4) Approximate curvature bulge over distance

drop ≈ d_total² / (2R_eff)

Here, R is Earth radius, k is the refraction coefficient, and h is the usable height after subtracting any clearance margin.

How to use this calculator

Select metric or imperial units.
Enter observer and target heights above the surface.
Keep the default Earth radius unless you need a custom value.
Choose no refraction, optical, radio, or a custom coefficient.
Enter clearance if terrain, Fresnel, or safety margin matters.
Adjust graph range and steps for the target-height plot.
Press Calculate line of sight to show results above the form.
Use the CSV or PDF buttons to save the current output.

Frequently asked questions

1) What does line of sight distance mean?

It is the maximum direct viewing or signal path between two heights before Earth curvature blocks the path. Atmospheric refraction can extend the range slightly by bending rays downward.

2) Why are two heights needed?

Each object has its own horizon distance. The total visible or reachable line of sight is the sum of the observer horizon and the target horizon.

3) What is the difference between optical and radio refraction?

Optical paths bend slightly in air, but radio links often use a stronger standard correction. That increases effective Earth radius and usually increases the calculated horizon distance.

4) What does the custom refraction coefficient do?

It lets you model nonstandard atmospheric conditions. Higher values increase effective Earth radius and extend the apparent horizon, while lower values reduce the correction.

5) Why add a clearance value?

Clearance reduces usable height before calculation. It is helpful when you want a conservative answer that accounts for terrain margins, obstacles, or engineering allowances.

6) Is this exact for real terrain?

No. It assumes a smooth spherical Earth and ignores hills, buildings, trees, and diffraction. Use it for planning, screening, and quick engineering estimates.

7) Can I use this for drone, tower, and marine visibility?

Yes. It works for any two elevated points when curvature matters. Common uses include observers, antennas, towers, ships, drones, and coastal viewpoints.

8) Why are surface arc distance and straight distance different?

The straight result is the tangent-based line-of-sight reach. The surface arc follows the curved Earth surface, so it is slightly different and useful for map-style interpretation.

Notes

For short distances and small heights, the simplified approximation d ≈ √(2Rh) is often close. This page uses the fuller expression with optional refraction and clearance handling.