Horizon Distance Calculator
Standing on a beach or a mountaintop? Enter your eye height above the ground and see exactly how far the horizon is — with the classic 3.57×√h formula and a dip-angle readout.
How to use this tool
Your eye level above the surface, in meters or feet.
See the distance in km and miles instantly.
Learn how far below level the horizon sits from your viewpoint.
What people use this tool for
Know how far you can see from a summit.
Plan sunrise/sunset shots with the true horizon distance.
Estimate when a distant lighthouse or ship appears over the horizon.
How it's calculated
For a spherical Earth of radius R and eye height h, the geometric horizon distance is d = √(2Rh + h²), which simplifies to about 3.57×√h (h in meters, d in km). The dip angle is arccos(R/(R+h)). Standard atmospheric refraction is not included, which would extend the visible horizon by roughly 8%.
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Frequently asked questions
What is the formula for horizon distance?
d = 3.57 × √h, where h is eye height in meters and d is in kilometers — derived from Earth's 6,371 km radius.
How far is the horizon at eye level on a beach?
At about 1.7 m eye height, the horizon is roughly 4.7 km (2.9 miles) away.
What is the dip angle?
The angle below true horizontal that you must look down to see the horizon — it grows with height.
Does refraction change the result?
Yes — normal atmospheric refraction extends the visible horizon by about 8%; this calculator shows the geometric value.
Can I enter height in feet?
Yes — toggle between meters and feet; the result shows both km and miles.
How far can you see from Mount Everest?
From the 8,849 m summit, the geometric horizon is about 336 km away.
Why does the horizon look farther at sea?
Flat open water has no obstructions, so you see the full geometric horizon.
Does this prove Earth is round?
The horizon's existence and its predictable distance from height are direct consequences of Earth's curvature.