Model Earth curvature effects on visibility paths fast. Switch units, heights, and refraction assumptions freely. Get clear distance results for surveying and radio work.
This calculator models a curved Earth using an effective radius: Reff = k · R, where R is the planet radius and k accounts for atmospheric refraction.
Notes: Terrain, buildings, and Fresnel-zone clearance are not included. For safety margins, increase heights beyond the computed “raise each end” value.
| Scenario | Height 1 (m) | Height 2 (m) | k | Approx. total LOS (km) |
|---|---|---|---|---|
| Two short towers | 30 | 20 | 1.3333 | ≈ 32.3 |
| Observer + hilltop | 1.8 | 150 | 1.0000 | ≈ 47.9 |
| Radio link planning | 60 | 60 | 1.3333 | ≈ 56.3 |
Values are rounded to show typical scale and will vary with radius and refraction settings.
Line of sight (LOS) distance is the maximum straight-path visibility between two points before spherical curvature blocks the view. It supports quick checks in surveying, coastal observation, aviation spotting, and early radio planning. Terrain, buildings, and vegetation are not included.
Curvature depends on the planet radius R. For Earth, a practical mean value is about 6371 km. The calculator also uses an effective radius Reff = k·R to model refraction; higher k reduces apparent curvature and increases predicted LOS distance.
For height h above the local surface, the horizon distance is d = √(2Reffh + h²). When h ≪ R, the h² term is tiny and d grows roughly with √h. This creates diminishing returns, but even modest height increases can extend visibility noticeably.
With two elevated endpoints, a common geometric estimate is dtotal = d(h₁) + d(h₂). It is a fast feasibility screen for whether towers can “see” each other over curvature. Use it as an upper bound until terrain profiles and obstacles are evaluated.
Clearance mode checks if the straight chord between endpoints intersects the curved surface for path length D. The midpoint bulge is bulge = Reff − √(Reff² − (D/2)²). The tool compares this bulge to the chord midpoint height (h₁ + h₂)/2 to report clearance.
Enter heights in meters, kilometers, or feet, and display distances in kilometers, meters, miles, or nautical miles. Keep height references consistent: use antenna height above local ground at each site, or convert all values to a single datum before comparing results.
A person near 2 m height has a horizon of only a few kilometers. Towers around 30–60 m commonly reach tens of kilometers, and two similar towers can nearly double the single-site horizon estimate. Refraction with k near 4/3 often adds useful margin.
Use these outputs as a first-pass constraint before detailed analysis. For radio links, add Fresnel-zone clearance and a full link budget; for surveying, include terrain and obstruction checks. Export CSV or PDF to record radius, k, units, heights, and safety margins, then validate borderline paths with terrain data. Keep assumptions consistent across all project documents today.
It is the straight geometric path between two points, ignoring terrain and obstacles. The calculator tests whether Earth curvature alone blocks that straight path for the selected heights and distance.
In many radio conditions, atmospheric refraction bends waves downward, behaving like a larger Earth radius. A common engineering approximation is k ≈ 4/3, which increases the radio horizon versus no-refraction geometry.
No. This tool models curvature and basic refraction only. Hills, buildings, trees, and mountains can block LOS well before curvature does, so profile data is still required for final validation.
Use antenna or eye height above the local ground at each endpoint. If you use elevations above sea level, you must convert both ends consistently and include tower height relative to that datum.
Negative clearance means the Earth bulge at the midpoint rises above the straight chord between endpoints. Increasing one or both heights, shortening the path, or using a larger k can restore clearance.
Yes. Set the planetary radius in kilometers. The same geometry applies, but atmospheric refraction behavior differs by composition and pressure, so choose k carefully or set k = 1 for vacuum-like conditions.
No. Link quality also depends on frequency, transmit power, antenna gains, Fresnel‑zone clearance, interference, and weather. Use this calculator as a first check, then perform a full link budget.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.