Distance to the horizon calculator
Enter the height of your eyes above the water or flat ground, and optionally the height of a lighthouse, ship or building. The calculator shows how far the horizon is and from how far the top of the object rises above it, in kilometres, miles and nautical miles.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose metres or feet.
- Enter how high your eyes are above the sea or flat ground – on a beach about 1.7 m, on a cliff add the cliff height.
- Optionally enter the height of the thing you want to see: a lighthouse, a mast, a mountain top.
- Read the distance to your horizon and the greatest distance at which the object’s top still shows.
d = √(h × (2R′ + h))
h is the height in metres, R = 6,371.0088 km the mean radius of the Earth, and R′ = R without refraction or 7/6 × R with standard refraction. The distance is along the line of sight; for any height you can climb, it is practically the same as the distance along the ground.
For an object of height H, its top is visible while the distance is less than d(h) + d(H).
Worked example
Eyes 1.7 m above the sea, with refraction: R′ = 6,371,008.8 × 7/6 = 7,432,843.6 m, so
d = √(1.7 × (2 × 7,432,843.6 + 1.7)) = √25,271,671 = 5,027 m → 5.03 km, 3.12 miles or 2.71 NM.
Without refraction it is 4.65 km. A 100 m tower has its own horizon at 38.56 km, so its top shows from up to 5.03 + 38.56 = 43.58 km.
Tips
- Height is measured above the water or the flat ground in front of you, not above sea level when you stand inland on a plateau.
- Hills, waves and haze shorten what you actually see.
- For radio links the commonly used factor is 4/3 instead of 7/6, which gives longer distances; this calculator uses the optical value.
Frequently asked questions
How far is the horizon at sea level?
For an adult standing on a beach with eyes about 1.7 m above the water, the horizon is about 5 km (3.1 miles) away with normal refraction, or 4.65 km by pure geometry. At 100 m it is about 38.6 km.
What is atmospheric refraction and should I include it?
Air is denser near the ground, so light bends slightly downward and you see a little beyond the geometric horizon. The usual standard assumes an Earth radius 7/6 times the real one, which makes the horizon about 8 % farther. Leave it on for real-world sightings; turn it off for pure geometry.
From how far can I see a lighthouse or a ship?
Add the horizon distance from your eye to the horizon distance from the object's top. The top of a 100 m tower seen from 1.7 m is visible up to about 43.6 km away; beyond that it is hidden behind the curve of the Earth.
Is there a simple rule of thumb?
With refraction, the distance in kilometres is about 3.86 × √(height in metres); geometrically about 3.57 × √h. In miles and feet: about 1.32 × √(height in feet) with refraction and 1.22 × √h without.
Why can I sometimes see much farther?
Temperature inversions over cold water can bend light far more than the standard assumption (looming and mirages), and haze often limits what you see long before the horizon. The calculator gives the standard case.