Horizon Distance Calculator
By Marko Visic · Updated Oct 7, 2026
How far can you actually see? Enter your eye-height — or tap a preset — for the distance to the horizon in miles, kilometers, and nautical miles, drawn as a circle on the map and refraction-corrected by default.
How far can you see, really?
At sea level with normal eye-height, the horizon sits about 3.1 miles (5 km) away — closer than most people guess. The number falls straight out of geometry: form a right triangle with the Earth's centre, your eye, and the tangent point on the sphere's surface, then read the tangent leg with d = √(2·R·h + h²). At 1.7 m height that gives 4.65 km geometric, or 5.0 km after standard atmospheric refraction (k = 0.13) bends the light just over the curve.
Climb up and the horizon moves out fast — but not as fast as you might think. Doubling your eye-height multiplies the horizon distance by only √2 (≈1.41), because the geometry is square-root. So a 100 ft tower buys you just √(100 / 5.5) ≈ 4.3× the eye-level horizon, not 20×. That non-linearity is why a 50 m lighthouse is enough to dominate a coastline (~25 km useful range) without needing the lighthouse to be a kilometre tall.
At commercial-flight altitude (35,000 ft / 10.7 km), the horizon sits ~245 mi / 396 km away with refraction. From Mt Everest's summit it's ~224 mi / 360 km. From the International Space Station at 400 km altitude, the geometric horizon is at the geodesic distance of about 1,368 mi / 2,201 km — a quarter of the way around Earth, but still far short of seeing the entire planet at once.
How to use the horizon distance calculator
Six steps from blank input to a refraction-corrected horizon read-out.
- Pick the mode. Single-observer mode (default) computes the horizon distance and dip angle for one location. Two-point visibility mode answers "can A see B?" given each point’s height. Toggle the segmented control at the top.
- Set your eye-height. Type your height above sea level (feet or meters) or pick a preset — standing (5.6 ft), lifeguard tower (15 ft), 10th floor (100 ft), Empire State deck (1,050 ft), airliner (35,000 ft). The math is identical for an observer’s eye 1.7 m above flat water and a sensor 1.7 m above flat ground.
- Choose refraction or geometric. Standard atmospheric refraction (k = 0.13) bends light over the horizon and adds about 7.2 % to the geometric distance — that’s why a paper-chart "5 km" horizon turns into a real 5.4 km. Toggle to "Geometric only" if you want pure spherical-Earth math (used in physics homework and some surveying applications).
- Set a location (optional in single mode). Search a city, address, or landmark; tap "Use my location" for GPS; or click anywhere on the map. The blue circle drawn on the map is the geodesic horizon — every point on that ring is the maximum theoretical line-of-sight distance from your eye at the chosen height.
- Read the headline numbers. Two result cards: Horizon Distance (in your chosen unit, with all three units in the subtitle) and Dip Angle (how far below true horizontal the horizon appears, in degrees and arcminutes). A schematic side view under the map shows the eye-height, the Earth curve, and the sight line grazing the horizon.
What people use a horizon distance calculator for
Seven common use cases — each one needs more than a half-remembered "3 miles to the horizon" rule of thumb.
Photography — overlook scouting and lens reach planning
Landscape and travel photographers use horizon distance to plan which mountains, coastlines, or skylines are technically visible from a chosen overlook. Standing at Mt Tamalpais (785 m) above San Francisco Bay, the geometric horizon sits at ~100 km — meaning the Farallon Islands (~50 km away) are easily within line-of-sight, while Big Sur (~165 km) is over the curve and invisible. Pair the result with focal-length math (object size in pixels = focal × physical size / distance) to know whether a 600 mm lens will resolve the target as more than a smudge.
Aviation — pilot horizon visibility and descent profile
For pilots, horizon distance is the radius of the visual horizon as seen from the cockpit. At 35,000 ft (~10.7 km) altitude with standard refraction, the horizon sits at ~396 km / 246 mi away — meaning a thunderstorm cell 200 km from your route is visible above the cloud deck while still ~170 km from your nearest pass. The dip angle (3.4° at 35,000 ft) is also the artificial-horizon offset that attitude indicators are calibrated to, and it sets the geometry for descent planning when targeting a runway visible at the limit of sight.
Maritime — lookout range and lighthouse design
Ship lookouts have used the formula d (nautical miles) ≈ 1.17 × √h(ft) for centuries — that’s our refraction-corrected horizon distance simplified into a single multiplier. A bridge wing 25 m above the waterline sees the horizon at ~19.2 km / 10.4 nm; a small fishing boat at 3 m sees only ~6.6 km / 3.6 nm. Lighthouse engineers stack focal-plane height and the receiver’s eye height: a 50 m lighthouse seen by a 5 m bridge is visible at √(2·R·50) + √(2·R·5) ≈ 25 + 8 = 33 km. Use the two-point visibility mode for that exact calculation.
Hiking — peak-to-peak visibility
Hikers planning long-line summit photography or amateur-radio "summit-on-the-air" contacts want to know whether two peaks can see each other. Two-point mode answers this directly: enter both summits and their elevations, get a yes/no with a "margin" reading that tells you how far over (or under) the curvature line the visibility falls.
Architecture — view marketing and observation deck design
Marketing copy for tall residential towers ("see all the way to Long Island from the 70th floor") needs a defensible horizon-distance citation. A 70th-floor unit at ~250 m elevation has a refraction-corrected horizon at ~60.7 km / 37.7 mi. For observation decks, designers also use dip angle to calibrate the railing angle and the camera-stand tilt, so visitors’ photos frame the sea-level horizon naturally instead of pointing slightly above into the sky.
Astronomy and amateur radio — line-of-sight to a distant antenna
VHF/UHF amateur-radio operators chasing tropospheric ducting, microwave-link engineers, and amateur astronomers checking observatory mountain visibility all need answers to "is X visible from Y given those two heights?" The two-point mode is the direct answer: it computes each point’s horizon distance, sums them, compares to the great-circle separation, and tells you whether the geometric line-of-sight clears Earth’s bulge. (For mission-critical RF planning use a proper Fresnel-zone clearance calculator that also models terrain — this tool covers the spherical-Earth baseline.)
Surveying and radio engineering — tower-to-tower line-of-sight check
Wireless ISPs, public-safety radio engineers, and microwave backhaul planners need to confirm that two proposed towers can see each other across the curve before they spend on terrain analysis. A 30 m tower seeing a 50 m tower has combined horizon ~45 km with refraction. If the towers are 35 km apart, you have a 10 km clearance buffer for terrain obstacles; if they’re 60 km apart, the towers will need to be taller. The two-point mode gives the first-pass yes/no in five seconds before anyone opens RadioMobile or TIA-222 software.
Heights reference table — kid eye-level to ISS orbit
Pre-computed horizon distances for twenty common observer heights, with both geometric (no atmosphere) and refraction-corrected (standard atmosphere) results. Dip angle in the last column is the angle below true horizontal at which the horizon appears.
| Vantage point | Height | Geometric | With refraction | Dip angle |
|---|---|---|---|---|
| Toddler eye-level | 0.9 m / 3 ft | 3.4 km / 2.1 mi | 3.6 km / 2.3 mi | 0.030° |
| Adult eye on beach | 1.7 m / 5'7" | 4.7 km / 2.9 mi | 5.0 km / 3.1 mi | 0.041° |
| Rider on horseback | 2.4 m / 8 ft | 5.5 km / 3.4 mi | 5.9 km / 3.7 mi | 0.049° |
| 2-story window | 6 m / 20 ft | 8.7 km / 5.4 mi | 9.4 km / 5.8 mi | 0.078° |
| 3-story building | 10 m / 33 ft | 11.3 km / 7.0 mi | 12.1 km / 7.5 mi | 0.101° |
| Lighthouse focal plane | 15 m / 50 ft | 13.8 km / 8.6 mi | 14.9 km / 9.3 mi | 0.124° |
| Tall tree / mast | 30 m / 100 ft | 19.6 km / 12.2 mi | 21.0 km / 13.1 mi | 0.176° |
| Cruise-ship bridge | 40 m / 130 ft | 22.6 km / 14.0 mi | 24.3 km / 15.1 mi | 0.203° |
| Eiffel Tower top | 324 m / 1,063 ft | 64.3 km / 39.9 mi | 69.1 km / 42.9 mi | 0.578° |
| Empire State observation | 381 m / 1,250 ft | 69.7 km / 43.3 mi | 74.9 km / 46.6 mi | 0.627° |
| Burj Khalifa top | 828 m / 2,720 ft | 102.7 km / 63.8 mi | 110.4 km / 68.6 mi | 0.924° |
| Hot-air balloon | 914 m / 3,000 ft | 107.9 km / 67.1 mi | 115.9 km / 72.0 mi | 0.971° |
| Pikes Peak summit | 4,302 m / 14,114 ft | 233.9 km / 145.3 mi | 251.4 km / 156.2 mi | 2.106° |
| Mt Everest summit | 8,848 m / 29,032 ft | 335.8 km / 208.6 mi | 360.8 km / 224.2 mi | 3.022° |
| Commercial cruise | 10,668 m / 35,000 ft | 368.7 km / 229.1 mi | 396.2 km / 246.2 mi | 3.318° |
| Concorde cruise | 18,288 m / 60,000 ft | 482.7 km / 300.0 mi | 518.7 km / 322.3 mi | 4.343° |
| U-2 spy plane | 21,336 m / 70,000 ft | 521.1 km / 323.8 mi | 560.0 km / 348.0 mi | 4.689° |
| High-altitude balloon | 36,576 m / 120,000 ft | 682.3 km / 424.0 mi | 733.2 km / 455.6 mi | 6.140° |
| Karman line | 100 km / 62 mi | 1,131 km / 703 mi | 1,215 km / 755 mi | 10.13° |
| ISS orbit | 400 km / 250 mi | 2,201 km / 1,368 mi | — | 19.79° |
The math behind the result
Three formulas drive every result this tool produces. All three model Earth as a smooth sphere of radius R = 6,371 km (the IUGG mean Earth radius).
1. Geometric horizon distance
Drop a perpendicular from your eye at height h to a tangent line touching the sphere at the visual horizon. The tangent length is d_geom = √(2·R·h + h²). For everyday heights (h ≪ R) the h² term is tiny and the formula collapses to the textbook approximation d ≈ √(2·R·h) ≈ 3.57·√h(m) km. At extreme heights (above ~100 km) we switch to the exact geodesic-arc formula d_arc = R · arccos(R / (R + h)), which measures the great-circle distance along the sphere's surface from your sub-observer point to the tangent point — the more meaningful answer when you're looking at a curved horizon from orbit.
2. Refraction correction
Light from beyond the geometric horizon doesn't go straight: it bends slightly downward through the dense lower atmosphere and reaches your eye even though the geometric line of sight would be blocked by the bulge. The standard atmospheric refraction coefficient k = 0.13 (used by ICAO, FAA, and surveying standards) means the effective Earth radius is R/(1 − k) ≈ 1.149 R, which is mathematically equivalent to multiplying the geometric horizon distance by 1/√(1 − k) ≈ 1.0721. So the practical horizon is ~7.2 % farther than the spherical-Earth answer. Real-world conditions vary — see the k-table below.
3. Dip angle
Dip is the angle between true horizontal (parallel to the local geoid) and the line of sight to the horizon. From the same right triangle: dip = arccos(R / (R + h)). At eye-level (1.7 m) the dip is 0.041° — too small to see directly. At 35,000 ft cruise altitude it's 3.3°, which is why pilots see the horizon visibly below the aircraft attitude reference. Maritime celestial navigators using a sextant must subtract the dip from the measured altitude of the sun to get the true altitude.
Standard atmospheric k-value reference
The refraction coefficient k varies with weather and time of day. This table covers the common conditions surveyors and meteorologists use:
| Conditions | k | Multiplier | Note |
|---|---|---|---|
| Vacuum / no atmosphere | 0.000 | ×1.0000 | Pure geometric — Moon, Mars without atmosphere. |
| Cold air, heavy mirage layer | −0.10 to 0.00 | ×0.95–1.00 | Mirage / "looming" — horizon appears closer than geometric. |
| Standard atmosphere (sea level, 15 °C) | 0.13 | ×1.0721 | ICAO / FAA / surveying default. Used by this tool. |
| Warm humid summer day | 0.15–0.18 | ×1.08–1.10 | Refraction slightly stronger than standard. |
| Strong temperature inversion | 0.20–0.30 | ×1.12–1.20 | Looming — distant ships appear above horizon. |
| Anomalous superrefraction | 0.50+ | ×1.4+ | Rare ducting events — extreme over-the-horizon visibility. |
Why is the horizon farther than you think?
Three reasons people lowball the answer: (1) the "3 miles to the horizon" rule of thumb is a flat-Earth heuristic that comes from medieval seafarers — it's actually a refraction- corrected eye-level value, but most people assume it's the maximum distance any human ever sees. (2) Most people don't intuit the square-root scaling. Doubling your eye-height only adds ~41 % to the horizon distance, which feels much less than "you doubled your height" suggests. (3) Atmospheric refraction extends the horizon by ~7.2 % beyond pure geometric in standard conditions, and by 10–20 % in temperature-inversion conditions.
The refraction effect is what makes the "flat earth" observational anomalies that conspiracy theorists cite happen in the first place — they cite a still-water lake photograph that should have hidden a distant lighthouse below the curve, but the photograph shows the lighthouse's base. The explanation isn't that Earth is flat; it's that on a calm sunlit day with warm air over cooler water you get a temperature inversion, k jumps from 0.13 to 0.30+, and the horizon extends 15–20 % farther than the textbook value. This calculator's standard k = 0.13 is the typical-day baseline; if you want to model anomalous propagation, swap in a higher k mentally.
Famous horizon distances
Six benchmark answers worth memorising — useful for trivia, photography, and sanity-checking your own calculations.
| Vantage point | Refraction-corrected horizon distance |
|---|---|
| Standing on a beach (5'7" eye) | ~3.1 mi / 5 km |
| Top of Empire State Building (1,250 ft) | ~46 mi / 75 km |
| Mt Everest summit (29,032 ft) | ~224 mi / 360 km |
| Cruising at 35,000 ft | ~246 mi / 396 km |
| Concorde at 60,000 ft | ~322 mi / 519 km |
| From the ISS (250 mi orbit) | ~1,368 mi / 2,201 km |
SimpleMapLab vs other horizon distance calculators
Most online horizon-distance tools are formula-only (input height, output distance) with no map view and no two-point mode.
Where SimpleMapLab adds value is the map view (you can see the horizon circle on Earth, not just read a number), the schematic side view (eye-height, the curve, and the sight line grazing the horizon), and the two-point mode (the "can A see B?" question is what most real-world users actually want to answer). We also default to refraction-corrected results, which is what surveyors, pilots, and sailors actually want — formula-only tools often skip refraction or hide it behind a checkbox most people never click.
Related tools and resources
For altitude above sea level (the height input this tool needs at terrain-bound observers), see Elevation Finder — it returns AWS Terrain Tiles elevation (USGS 3DEP / SRTM) for any point on Earth. For directional bearings between two points (which way is the horizon target?), see Bearing & Compass Calculator. For the great-circle distance between any two locations (the input to two-point visibility mode), see Distance Between Two Places. For the sun's position above the horizon at any time and place — directly related to sunrise/sunset visibility from elevated viewpoints — see Sun Position Calculator. To list every US city within a chosen radius, see Find Cities in Radius.
Frequently asked questions
Horizon-distance math: spherical Earth with R = 6,371 km (IUGG mean radius), formula d = √(2·R·h + h²) for everyday heights and d = R · arccos(R / (R + h)) at extreme altitudes. Refraction: standard atmosphere k = 0.13 (ICAO / FAA / surveying default), equivalent to multiplying geometric distance by 1.0721. Dip-angle formula: dip = arccos(R / (R + h)). Terrain viewshed: bare-earth line-of-sight over AWS Terrain Tiles (Mapzen “terrarium” PNGs merging USGS 3DEP in the US and SRTM elsewhere), sampled along 360 rays out to 200 km, curvature- and refraction-corrected with an effective Earth radius R / (1 − 0.13). Map basemap: OpenFreeMap Liberty vector tiles (free and unlimited). Geocoding for the location search: Photon (typo-tolerant autocomplete) and Nominatim(OpenStreetMap reverse geocoding for place labels). The horizon math and the terrain viewshed both run entirely client-side in your browser (the viewshed in a Web Worker) — no data leaves your device.
More SimpleMapLab tools
Find altitude above sea level for any point on Earth — AWS Terrain Tiles (USGS 3DEP / SRTM).
Initial, final, rhumb-line, and magnetic bearings between any two points.
Great-circle distance between any two points on Earth — multi-unit output.
List every US city within a chosen radius. Filter by population, export CSV.