Earth Curvature Calculator
The Earth Curvature Calculator shows exactly how much of a distant object the curve of the Earth hides. Type your eye height and the distance to a target — a ship, a lighthouse, a coastline — and instantly see the distance to the horizon, the geometric drop of the Earth's surface, and the obscured height that's physically out of sight. Use it as a quick distance to horizon calculator, a line of sight earth curvature calculator, or just to see how far you can really see. Runs entirely in your browser: no upload, no account, free.
How to Use the Earth Curvature Calculator
- Enter your observer height — how high your eyes are above the ground or water
- Enter the target distance — how far away the object you're viewing is
- Switch between Metric (m/km) and Imperial (ft/mi) at any time
- Optionally enable Atmospheric Refraction to account for the slight bending of light near the horizon
The three output cards — Distance to Horizon, Total Drop, and Obscured Height — recalculate on every keystroke. There's no submit button and nothing to upload. Because the refraction toggle and the height field are both built in, this doubles as an earth curvature calculator with refraction and an earth curvature calculator with elevation — no need to switch tools for either.
How Distance to the Horizon Is Calculated
The distance to horizon formula is d = √(h·(2R+h)), where h
is your eye height above the surface and R is Earth's radius (6,371 km). It comes straight
from the Pythagorean theorem applied to a line of sight tangent to a sphere.
At the calculator's default 1.7 m eye height — about average for a person standing at the shoreline — the horizon sits roughly 4.65 km (2.89 miles) away. Because the formula depends on the square root of height, gaining elevation extends your view fast without needing to go very high: standing on a 10 m platform pushes the horizon out to about 11.3 km.
Total Drop: How Much the Earth Curves Over Distance
Total Drop is the exact amount the Earth's surface falls away from a perfectly flat plane
over your target distance: drop = √(R²+d²) − R. At everyday distances this is extremely close
to the classic rule of thumb that the Earth curves about 8 inches per mile squared — and
because it scales with distance squared, the curve compounds quickly: roughly 8 inches at 1 mile, about
32 inches at 2 miles, and around 8 feet by 10 miles. That makes this a handy curvature of the
earth per mile calculator for surveying, RF line-of-sight planning, or settling an argument.
Obscured Height: Why Ships and Lighthouses Disappear Hull-First
Once your target is farther away than your own horizon distance, part of it drops below the line of sight — that's the Obscured Height card. It's the classic reason ships disappear hull-first over the horizon: the low hull is hidden by the curve before the taller masts or superstructure are, which is one of the oldest visual demonstrations that the Earth is round rather than flat.
Example: at a 1.7 m eye height watching a ship 10 km away, about 2.24 m of its hull is already hidden below the horizon — even though the ship itself hasn't moved any closer to "sinking."
Atmospheric Refraction: Why the Horizon Is a Little Farther Than Geometry Predicts
Air density changes with altitude, which bends light slightly and lets you see a bit farther than pure geometry predicts. Surveyors and navigators commonly model this with an effective Earth radius of 7/6 (about 1.167×) the true radius — flip on the Atmospheric Refraction toggle to apply that same standard correction. It pushes the horizon distance out and very slightly reduces the obscured height at any given distance.
Frequently Asked Questions
How do you calculate the distance to the horizon?
The distance to the horizon formula is d = √(h·(2R+h)), where h is your eye height above
the surface and R is Earth's radius (6,371 km). At a typical 1.7 m eye height, that works out to about
4.65 km (2.89 miles) before the curve of the Earth blocks your line of sight.
How much does the Earth curve per mile?
The Earth curves about 8 inches per mile squared — a small-angle approximation of the exact drop
formula, drop = √(R²+d²) − R. Because it scales with distance squared, the curve compounds
fast: about 8 inches at 1 mile, but roughly 32 inches at 2 miles and 8 feet at 10 miles.
Why do ships disappear hull-first over the horizon?
A ship's hull sits lower than its masts, so the curvature of the Earth hides the hull before it hides the taller superstructure — the classic visual proof that the Earth is curved, not flat. This calculator's Obscured Height card shows exactly how much of a target that height is hidden at any distance.
Does atmospheric refraction affect how far you can see?
Yes. Light bends slightly as it passes through air of varying density near the surface, which pushes the visible horizon a bit farther than pure geometry predicts. Surveyors and navigators commonly approximate this using an effective Earth radius of 7/6 (about 1.167×) the true radius — the Atmospheric Refraction toggle in this calculator applies exactly that correction.
How far away is the horizon at sea level?
For an average adult's eye height of about 1.7 m standing at the shoreline, the horizon is roughly 4.65 km (2.89 miles) away. Standing higher — on a cliff, a boat's deck, or a lighthouse — pushes the horizon much farther, since horizon distance grows with the square root of your height.
Does observer height change how far you can see?
Yes, substantially. Because the horizon distance formula depends on the square root of your height, even a modest gain in elevation extends your view a lot — climbing from 1.7 m to 10 m eye height roughly triples the distance to the horizon, from about 4.65 km to 11.3 km.
