Can two points see each other?
The farthest two raised points can see each other over the Earth's curve, and for a given distance whether they can, the clearance at the midpoint, and how much of the far target is hidden.
Planning and education aid. Not for primary navigation. Full disclaimer
They can see each other up to 32.47 km apart.
- This assumes a smooth Earth: terrain, buildings, and trees can block the view or the signal.
- Observer's horizon
- Visible at this distance
- Hidden height of the target
- Clearance at the midpoint
Provenance
- Computed by
- navigation.los.visibility 1.0.0, core 0.1.0
- Model
- Spherical Earth, R = 6371000 m, refraction k = 0.13 (effective radius 7322989 m)
- Accuracy
- Exact for the model; real refraction varies with the weather
- Notes
- 1 shown with the answer
- Cites
- National Geospatial-Intelligence Agency, Pub. No. 9, The American Practical Navigator (Bowditch)
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Spherical Earth with effective radius R/(1 − k)
Accuracy: Exact for the model; real refraction varies with the weather
When to use this: Use this to ask whether the curve of the Earth alone puts something out of sight: a light or a landmark from a bridge wing, a tower from a receiver, an aircraft from a ground station, a drone from its pilot. Give both heights for the range at which they lose each other, and add a distance to be told whether they can see each other at it, how much of the far object is cut off below the horizon, and how much room the sightline has over the bulge halfway between them.
Limitations: This is the curve of the Earth and nothing else. There is no terrain in it, no buildings, no trees: a hill between the two points blocks a sightline this tool calls clear, which is why every answer carries the terrain warning. It is geometry rather than propagation, so it says nothing about whether a radio link closes or a light is bright enough to see at the range it gives — for a radio path the first Fresnel zone wants more clearance than a bare sightline, which is the neighbouring tool. Refraction enters only through the coefficient k, held at a nominal 0.13; real air varies, and a temperature inversion over water can lift a target well beyond the range given here.
Worked example: From 2 m, a target 30 km away. Source: Bowditch's own procedure, the distance to each horizon added together: the tool's range is that sum over 115 pairs of heights printed in NGA Pub. 9 Table 12, within the tenth of a nautical mile the table rounds to plus the 0.231% by which its square-root rule sits above the exact horizon. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Distance between them
- 30 km
- Observer height
- 2 m
- Target height
- 50 m
You get
- Farthest mutual visibility
- 32.47 km
- Observer's horizon
- 5.41 km
- Visible at this distance
- yes
- Hidden height of the target
- 41.3 m
- Clearance at the midpoint
- 10.6 m
Review: Not yet independently reviewed by a geodesist.
Last verified: 2026-09-19, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Checked against: 23 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- The American Practical Navigator (Bowditch), National Geospatial-Intelligence Agency, Pub. No. 9, 2024 edition. Volume II, Table 12 (Distance of the Horizon) and Table 14 (Dip of the Sea Short of the Horizon).