How far away is the horizon?

For a person standing at the beach with eyes about 1.7 metres above sea level, the geometric horizon is roughly 4.65 km away. With atmospheric refraction included (light bends slightly around the Earth's curvature), the visible horizon is a little further, around 5.0 km. The distance increases with the square root of your height, so doubling your height only increases the horizon distance by about 41 percent, not double.

What formula is used to calculate distance to the horizon?

The basic geometric formula is d = square root of (2 x R x h), where R is the Earth's radius (about 6,371 km) and h is your eye height above the surface, in the same units. A more precise version accounting for atmospheric refraction multiplies the effective Earth radius by about 1.07 (a factor of 7/6), which slightly increases the calculated distance. In practical units, this simplifies to roughly d (km) = 3.57 x square root of h (metres) for the pure geometric case, or about 3.86 x square root of h (metres) with refraction included.

Does height above sea level really change how far you can see?

Yes. Because the Earth curves away from an observer, higher vantage points let you see further before the horizon drops below your line of sight. Someone standing at 1.7 m sees about 5.0 km. From the top of a 100 m tall building, the horizon extends to about 38.6 km. From a commercial aircraft cruising at 10,000 m, the horizon is over 385 km away. This is why lighthouses, watchtowers and observation decks are built as tall as practical.

Distance to Horizon Calculator

Work out how far away the horizon is based on your height above the ground or sea level. This calculator uses the standard geometric horizon formula, with and without a correction for atmospheric refraction.

Enter your eye height, or pick a common vantage point, to see the horizon distance in kilometres, metres and nautical miles.

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Reference formula Standard geometric horizon distance formula, Earth radius 6,371 km.

1. Your Height

Common vantage point (or choose custom)

Eye height / altitude above the surface

Height unit

2. Distance Units

Preferred distance unit for results

The geometric horizon assumes light travels in a straight line. In reality, Earth's atmosphere bends light slightly, letting you see a little further than pure geometry predicts. The refraction-corrected figure is the more realistic estimate of what you can actually see.

Distance to the Horizon

Your Height

Above sea level / ground

Geometric Horizon

Straight-line-of-sight formula

Visible Horizon (with refraction)
-
More realistic estimate

Refraction Adds

Extra visible distance

Horizon Distance at Common Heights

Vantage Point	Height	Geometric Horizon	With Refraction

Calculation Breakdown

Height above surface-

Earth radius used6,371 km

Geometric formulad = √(2Rh)

Geometric distance-

Refraction factor7/6 (approx 1.07x radius)

Visible distance (refraction-corrected)-

Distance in Other Units

Geometric horizon (km)-

Geometric horizon (miles)-

Geometric horizon (nautical miles)-

Visible horizon (km)-

Visible horizon (miles)-

Visible horizon (nautical miles)-

Summary: Enter your height above the surface.

How the Distance to the Horizon is Calculated

The horizon is the point where the Earth's curved surface drops below your line of sight. The higher you are, the further away that point is, because you can see further around the curve of the planet before it falls away. This calculator uses the standard geometric formula for horizon distance, based on your height above the surface and the radius of the Earth.

The Geometric Formula

The basic geometric distance to the horizon is:

d = √(2 × R × h)

Where d is the distance to the horizon, R is the radius of the Earth (approximately 6,371 km), and h is your height above the surface, in the same units as R. This formula comes from a simple right-angle triangle: your eye, the centre of the Earth, and the point on the horizon form a triangle where the line of sight is tangent to the Earth's surface. Because h is tiny compared to R, the formula simplifies to d approximately equal to the square root of 2Rh.

Correcting for Atmospheric Refraction

Light does not travel in a perfectly straight line through the atmosphere. Air density decreases with altitude, which bends (refracts) light slightly downward as it travels long distances close to the surface. This effect lets you see a little further than the pure geometric formula predicts. Surveyors and navigators commonly account for this using an effective Earth radius about 7/6 (roughly 1.07 times) the true radius, giving a refraction-corrected horizon distance a few percent greater than the simple geometric result. The exact amount of refraction varies with temperature, pressure and humidity, so this correction is a widely used average, not an exact value for every condition.

Worked Example

A person standing at the beach with their eyes 1.7 m above sea level has a geometric horizon distance of about 4.65 km. With the standard refraction correction (an effective Earth radius of 7/6 the true radius), the visible horizon extends to about 5.03 km, roughly 370 m further. This is why on a clear day at the beach, the horizon looks close, but climbing even a small dune or headland noticeably pushes it further away.

Why Height Matters More Than You Would Think

Because the formula depends on the square root of height, small increases near ground level make a noticeable difference, while very large increases in height give diminishing returns. Doubling your height from 1.7 m to 3.4 m increases the horizon distance by about 41 percent, not 100 percent. This is why lighthouses and observation towers are built tall: even a modest increase in height meaningfully extends the visible horizon, but each extra metre above that gives a smaller improvement.

Common Uses

Estimating how far out to sea a lighthouse or lookout can be seen from
Working out line-of-sight range for radio, radar or visual signalling
Understanding why ships appear to "sink" below the horizon as they sail away
Photography and surveying, when working out visible range from elevated positions
General curiosity about how far you can actually see from a given height

Related Calculators

Essential Calculators: browse all conversion and everyday tools.
Angle of Elevation Calculator: work out the angle to a distant or elevated object.
Air Pressure at Altitude Calculator: another calculator based on height above sea level.
km to Miles Converter: convert your horizon distance to miles.
Circumference Calculator: explore circle and curvature geometry.

Sources: Standard geometric horizon distance formula (d = √(2Rh)), used widely in navigation, surveying and optics references. Earth mean radius of 6,371 km (International Union of Geodesy and Geophysics). Atmospheric refraction correction factor of approximately 7/6, as commonly applied in surveying and marine navigation texts.

This calculator gives an estimate based on a spherical Earth model and an average atmospheric refraction correction. Actual visible distance can vary with atmospheric conditions, terrain, obstructions and the height and size of the object you are trying to see, and does not account for Earth's slight oblate shape.