Horizon Distance Calculator

In Earth's atmosphere, air density decreases with altitude. Light from the horizon travels through layers of decreasing density, bending (refracting) downward. This curves the effective line of sight slightly downward, allowing it to follow the curvature of the Earth more closely and extending the visible horizon. The standard approximation replaces Earth's radius with (7/6) R for typical atmospheric conditions.

Yes. Horizon distance scales as sqrt(h): doubling your height increases horizon distance by about 41% (sqrt(2) = 1.41). From the 443 m observation deck of the Empire State Building, the geometric horizon is about 75 km away (with refraction). From a commercial aircraft at 10,000 m altitude, the horizon is about 357 km away.

From the summit of Mount Everest (8,849 m), the horizon with refraction extends to about 336 km. In practice, atmospheric haze usually limits visibility much more than geometry. The clearest views from high altitudes can sometimes exceed 500 km in ideal dry conditions — but only by looking across the curved Earth rather than at a flat geometric horizon.

The dip angle is the angle between the true horizontal (perpendicular to gravity) and the line of sight to the visible horizon. When a navigator measures the altitude of the Sun above the visible horizon with a sextant, they must subtract the dip angle to get the altitude above the true horizontal — a critical correction for celestial navigation. Tables of dip angle by eye height (corrected for refraction) were standard nautical references.

The visual horizon at sea appears as a clean line because the ocean is flat. On land, irregular terrain breaks up the horizon line. The horizon actually dips below the true horizontal — it is always slightly below eye level by the dip angle. This is too small to notice without instruments at low heights but becomes perceptible at very high altitudes.

Radio waves (like microwaves used in cellular and satellite communications) travel in nearly straight lines and are blocked by Earth's curvature beyond the radio horizon. The radio horizon is typically extended by about 15% beyond the optical horizon due to atmospheric refraction of radio waves (larger than optical refraction). Line-of-sight radio links must account for Earth's curvature in tower placement and height calculations.

No. At ground level or even from a few hundred meters altitude, the visual field is too limited to perceive the curvature directly. The curvature becomes faintly perceptible at altitudes around 10,000 m (commercial aircraft altitude) under ideal conditions with a wide field of view. The dramatic curvature seen in early astronaut photographs is visible from altitudes above about 100 km (the Karman line into space).

The formula d = sqrt(2Rh) can be rearranged to R = d^2 / (2h). This means if you know how far the horizon is (by timing the disappearance of a ship) and your height, you can calculate Earth's radius. This was approximately done by ancient Greek scientists. Eratosthenes used the angle of sunlight at two points to calculate the circumference directly around 240 BCE.

A lighthouse has two relevant horizon distances: the geographic range (how far away the light can be seen geometrically, based on lighthouse height and observer eye height) and the luminous range (how far the light can be seen given its brightness and atmospheric visibility). The combined or nominal range is the greater of these. The horizon range for a 30 m lighthouse viewed from 5 m height: d = sqrt(2 x 6371 x 0.030) + sqrt(2 x 6371 x 0.005) = 19.5 + 8.0 = 27.5 km (geometric, no refraction).