Horizon Distance
Estimate how far you can see to the horizon based on height above the surface.
By Aryan Khan, Founder & Editor · Updated October 2026
For example, from a cruising airliner at 35,000 feet the geometric horizon lies about 369 km (229 miles) away — and the horizon itself dips some 3.3 degrees below horizontal.
How to use Horizon Distance
Height buys distance at a square-root exchange rate:
Horizon Distance estimates how far you can see to the horizon from a given height above the surface. Enter your height — eye level, a cliff, a tower, a summit — and read the distance to the horizon, with the standard-refraction figure beside it.
- 1Enter eye or observer height.
- 2Read distance to the horizon.
What people use Horizon Distance for
1. Viewing and photography planning
Summit-to-summit visibility, lighthouse ranges and skyline shots all start from two horizon distances added together — the Line of Sight Helper does the paired version.
2. Coastal and sailing questions
When will the lighthouse's lamp rise? Its light has its own horizon; yours and its sum is the sighting range — mariner's arithmetic, computed here.
3. Explaining the view
Why the sea's edge looks close from the beach (about 4.8 km) and enormous from the headland — height, square-rooted. The Hidden Height Calculator prices what the cut hides.
4. Tower and drone work
A 100 m mast commands a 35.7 km geometric horizon — coverage maps and camera plans start from that circle.
Worked examples
Eyes 1.8 m above the water: horizon 4.8 km geometric, about 5.2 km with standard refraction. The most local fact in geography — your personal edge of the visible world is a city walk away.
From the 1,917 m summit (6,288 ft), the geometric horizon runs 156 km — on the clearest days the Atlantic and four states argue within it, exactly as the mountain's fame claims.
Horizon distance by height
Computed geometrically (√(2Rh)) with the standard-refraction column beside it.
| Height | Geometric | With standard refraction |
|---|---|---|
| 1.8 m (standing eye) | 4.8 km | 5.2 km |
| 10 m (cliff path) | 11.3 km | 12.2 km |
| 30 m (small tower) | 19.6 km | 21.1 km |
| 100 m (skyscraper deck) | 35.7 km | 38.6 km |
| 1,000 m (hill summit) | 112.9 km | 121.9 km |
| 8,849 m (Everest) | 335.9 km | 362.8 km |
To see an object of height, add its horizon to yours: two 30 m towers can sight each other at 39.1 km — before terrain and weather vote.
Geometric horizon distance grows with observer height, but real visibility is usually shorter
On a spherical Earth, horizon distance can be estimated from observer height and Earth radius. The relationship is nonlinear, so raising the observer even modestly can noticeably increase the theoretical horizon distance.
Terrain, buildings, haze, refraction and weather alter what is actually visible. Use the result as geometric context, not as a guarantee of line-of-sight or a substitute for terrain-aware visibility analysis.
How to interpret the result
The most common errors come from using a correct result to answer the wrong geographic question. Keep these points in mind for Horizon Distance:
- Remember that elevation models see bare terrain: no buildings, no forest canopy. A line-of-sight 'clear' verdict can still be blocked by a wood, and a horizon distance assumes open ground — treat results as the terrain baseline, then add land cover from local knowledge.
- Include your height inputs explicitly (eye height, mast height, deck level) when sharing visibility results: the same hill answers differently for a child, an adult and a 10 m antenna, and unstated heights make numbers unreproducible.
Limits & appropriate use
Terrain intelligence carries one dominant limit: the model sees bare earth at ~90 m spacing with metres of vertical error, and is blind to canopies, walls and wires. Every downstream answer inherits it — profiles show terrain truth with noisy amplitude, line-of-sight verdicts are pending trees, horizons assume open ground, and solar radiation averages assume an unshaded panel. The second limit is temporal: climate letters and hardiness zones are thirty-year character, not this year's behaviour, and seismicity is a mood, not a hazard model. Each result here is printed with its recipe precisely so these boundaries travel with the number.
The value proposition is screening-grade truth at zero cost: orientation for sites, gardens, antennas, shoots and curiosity, with the upgrade points clearly marked. When money or safety attaches to the answer — tower siting, flood insurance, structural shading, avalanche terrain — the escalation is professional: licensed survey, certified shade studies, regulatory flood determinations and geological hazard services. A good free tool makes that ladder visible instead of pretending to be the top of it.
- Construction and tower siting → licensed topographic survey.
- Flood decisions → regulatory determinations (FEMA/FIRM in the US).
- Solar finance → certified shade and production studies.
Data & methodology
The workspace applies the square-root horizon approximation using Earth radius adjusted by a fixed refraction coefficient; terrain and atmospheric variation are not modelled.
For source details, licences and model limitations, see Data Sources and Methodology.
Key terms worth knowing
- Refraction coefficient
- The standard 0.13 factor bending sightlines over the curvature.
- Antipode
- The diametrically opposite point; latitude flips, longitude shifts 180°.
Editorial guidance: MapBench explains the method and limitations so the tool can be used as a transparent reference, not as a black-box answer. For legal boundaries, safety-critical routing, surveying, engineering, regulated decisions or official statistics, verify the result with the responsible authority or a qualified professional.
Category: Earth Science. Results are intended for everyday analysis and planning unless a page explicitly states otherwise.
Method, assumptions & limits
- This tool’s method
- The workspace applies the square-root horizon approximation using Earth radius adjusted by a fixed refraction coefficient; terrain and atmospheric variation are not modelled.
- Before relying on the answer
- Check the location, height units and any model options shown by this calculator. A terrain lookup and a geometric Earth model answer different questions.
- What the result cannot establish
- Local terrain, atmospheric conditions and source resolution can matter more than numerical rounding. Do not use a planning result for safety-critical work.
Coverage: Worldwide. Search, basemap and external data requests may use third-party services; browser-based does not mean every operation is offline. Read the source and licence notes, calculation methodology and privacy policy. If a result looks inconsistent, report a correction with the inputs and mode used.
Frequently asked questions
Clear answers about the calculation, accuracy and appropriate use.
Hills and haze?
This is geometric range; terrain and weather reduce real visibility.
Is this suitable for engineering or legal decisions?
Treat the result as planning or educational context unless the page explicitly says otherwise. Engineering, hazard and legal decisions should use authoritative specialist data.
Why can terrain data differ between sources?
Elevation and earth datasets vary in resolution, collection date and processing method. Small local features may not be represented equally.
Can I verify the data source?
Yes. MapBench documents major providers and methodology on the Data Sources and Methodology pages.
What is the dip of the horizon?
The angle below horizontal at which the horizon appears: about 0.043° (2.6 arcminutes) at eye level, growing to roughly 3.3° at airliner altitude. Surveyors and navigators correct for it — at sea level it is small, from a cockpit it is not.
Why two numbers — geometric and refraction?
Air bends light gently Earthward, extending the view (modelled as an Earth about 7⁄6 larger). The geometric figure is the guarantee; the refraction figure is the typical day. Exceptional days break both, upward.
Does eyesight or a telescope extend it?
No — optics sharpen what arrives; the horizon is set by geometry and your height alone. Only climbing extends it.
Binocular ships appear 'over' the horizon sometimes?
Refraction again: temperature layers can duct and lift images (superior mirage), letting light from below the geometric horizon reach you. The calculator's standard model is the average; the atmosphere freelances.
Freshwater horizons?
Identical — the Great Lakes' long sight lines are pure height-and-distance geometry over very flat water.
How far on the Moon?
Same formula, smaller radius (1,737 km): standing eye height gives about 2.4 km. Astronauts' horizons feel close for a reason.
Is the formula exact?
√(2Rh + h²) is exact for a sphere; the famous √(2Rh) shortcut differs by less than a metre until heights approach a kilometre. This page uses the full form.
Sunrise timing?
The visible sunrise comes early by roughly the dip's worth of Earth's rotation — about 2–3 extra minutes of daylight for a mountaintop observer versus the valley, horizon geometry again.
Related tools and resources
What the curve hides: the Hidden Height by Earth Curvature Calculator; radio version: the Radio Line-of-Sight Calculator; the drop: the Earth Curvature Calculator.
More free tools
Sources, methodology & editorial trust
- ✓ Browser-first processing where supported
- ✓ External sources are documented
- ✓ No account required for public tools
- ✓ Review data sources
Calculations are documented with their assumptions, limitations and source context rather than presented as unexplained answers.
Reviewed and maintained by Aryan Khan, Founder & Editor of MapBench.
Part of our distance calculators hub
Horizon Distance sits in the distance calculators cluster, alongside 28 other tools that answer neighbouring questions with different methods or datasets.
You may also need
When this answer is only part of the job, these clusters cover the next step.
Read the guide behind this tool
How Far Can You See? The Quiet Math of Horizons — From a beach, a cliff or a cabin deck: horizon distance, observer height and terrain all matter. A practical walk through visibility math.