Horizon Distance Calculator

How far can you actually see? Enter your eye-height (or pick a preset — beach, lighthouse, Empire State, jet cruise, ISS) and the tool computes the geometric horizon distance, the dip angle, and a list of US cities within direct line-of-sight. Two-point mode answers "can A see B?" given each location's height. Refraction-corrected by default for real-world results.

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 1,426 mi / 2,295 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.

1. Pick the mode. Single-observer mode (default) computes horizon distance, dip angle, and visible US cities for one location. Two-point visibility mode answers "can A see B?" given each point’s height. Toggle the segmented control at the top.
2. Set your eye-height. Type your height above sea level (feet or meters) or pick a preset — beach (1.7 m), lighthouse (15 m), Empire State Building (381 m), commercial flight (10,668 m), ISS (400 km). The math is identical for an observer’s eye 1.7 m above flat water and a sensor 1.7 m above flat ground.
3. Choose refraction or geometric. Standard atmospheric refraction (k = 0.13) bends light over the horizon and adds about 7.5 % 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).
4. 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.
5. Read the headline numbers. Three result cards: Horizon Distance (in your chosen unit, with all three units in the subtitle), Dip Angle (how far below true horizontal the horizon appears, in degrees and arcminutes), and Cities In View (US cities within direct line-of-sight, sorted by population).
6. Inspect the visible-cities list. When the observer is set in the US, the table lists every city within horizon range from the SimpleMaps city database — name, state, population, distance. Click "Show all N" to expand beyond the first 20. Outside the US, the list is empty (we don’t have a worldwide cities dataset of comparable accuracy).

What people use a horizon distance calculator for

Seven recurring patterns we see — each one needs more than a half-remembered "3 miles to the horizon" rule of thumb.

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.

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) ≈ 1.0746. So the practical horizon is ~7.5 % 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:

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 ~7.5 % beyond pure geometric in standard conditions, and by 10–20 % in temperature-inversion conditions — contributing to historical "impossible" observations like Theodore Roosevelt seeing Long Island from the Empire State Building roof (the geometric line says it's marginal; refraction makes it routine).

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.

SimpleMapLab vs other horizon distance calculators

Most online horizon-distance tools are formula-only (input height, output distance) with no map view, no two-point mode, and no list of visible places. We compared against the three most-cited free alternatives:

The other tools cover the basic formula well and are fine if all you need is a single number from a height. Where SimpleMapLab adds value is the map view (you can see the horizon circle on Earth, not just read a number), the two-point mode (the "can A see B?" question is what most real-world users actually want to answer), and the cities-in-view list (turns abstract distance into a concrete "you can see Newark and Yonkers from here" 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 Copernicus 30 m DEM elevation 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 enumerate every US city within a chosen radius (a strict superset of cities-in-view but without the line-of-sight cap), see Find Cities in Radius.

Frequently asked questions

More SimpleMapLab tools