UpToWhereEarth curvature and distance to horizon calculator
This page computes three things from your eye height: how far away your horizon is, how much of a distant object the curve of the Earth hides, and how far the surface drops below a flat line over any distance. It is free, works in metres or feet, and can include atmospheric refraction, which pushes the horizon about 8% further out than bare geometry.
- Geometric constant3.57 km per sqrt(metre)
- With refraction3.86, about 8% further
- Radio, 4/3 earth4.12
- CostFree, no sign-up
Earth curvature and distance to horizon
This is the geometry alone. It assumes nothing between you and the target, which is exactly the assumption real ground breaks.
What the horizon table assumes
Every number above comes from one equation. The horizon sits where your line of sight grazes the surface, which happens at a distance that grows with the square root of your height. Doubling your height buys 41% more horizon, not double.
Refraction is the second term and it is not a rounding error. Air thins with altitude, light bends gently downward as it crosses that gradient, and the sightline follows the curve a little way instead of leaving on a tangent. The standard allowance turns the 3.57 constant into 3.86.
| Your eye height | Horizon, geometric | With refraction |
|---|---|---|
| 1.7 m (5.6 ft) | 4.7 km (2.9 mi) | 5.0 km (3.1 mi) |
| 10 m (33 ft) | 11.3 km (7.0 mi) | 12.2 km (7.6 mi) |
| 30 m (100 ft) | 19.7 km (12.2 mi) | 21.3 km (13.2 mi) |
| 61 m (200 ft) | 27.9 km (17.3 mi) | 30.2 km (18.7 mi) |
| 100 m (328 ft) | 35.7 km (22.2 mi) | 38.6 km (24.0 mi) |
| 305 m (1,000 ft) | 62.3 km (38.7 mi) | 67.4 km (41.9 mi) |
| 1,000 m | 112.9 km (70.1 mi) | 122.1 km (75.9 mi) |
| 3,715 m (Teide) | 217.6 km (135.2 mi) | 235.3 km (146.2 mi) |
| 8,849 m (Everest) | 335.8 km (208.6 mi) | 363.2 km (225.7 mi) |
The row at 1.7 m is eye level for an adult of about 6 ft, which is why the beach answer is roughly 3 miles and not the 6 miles people expect.
Is the horizon 7 miles away, or 12?
Both, and neither. The question has no single answer because the horizon moves with your eyes, and every confident number you have read is really a statement about someone standing somewhere specific. Turned around, the same equation gives the height each famous figure needs.
| Horizon at | You have to be this high | With refraction |
|---|---|---|
| 7 mi (11 km) | 10 m (33 ft) | 9 m (28 ft) |
| 12 mi (19 km) | 29 m (96 ft) | 25 m (82 ft) |
| 20 mi (32 km) | 81 m (267 ft) | 69 m (228 ft) |
| 60 mi (97 km) | 732 m (2,401 ft) | 625 m (2,052 ft) |
Refraction lowers the height you need by about 14%, which is the same 8% extension seen from the other side.
Curvature drop is not hidden height
This is the single most common mistake in the argument, and it is worth being precise about. The familiar 8 inches per mile squared is a real formula and it is accurate: over 10 miles the surface really does fall about 20 m below a flat line drawn from where you stand. It is simply not the answer to the question people ask it.
Drop is measured from a tangent plane at your feet. What hides a distant object is measured from your eye, past your own horizon, which sits some distance away and eats most of the first part of the drop. An observer 1.7 m up looking at something 10 miles away loses about 12 m of it, not 20.
Put your height into the calculator and the hidden figure accounts for that. The gap between the two numbers is exactly the horizon distance of the observer, and it is why photographs of distant skylines rarely match a naive drop calculation in either direction.
| Distance | Drop, metres | Drop, feet |
|---|---|---|
| 1 mi | 0.20 m | 0.67 ft |
| 10 mi | 20 m | 67 ft |
| 50 mi | 508 m | 1,667 ft |
| 100 mi | 2,032 m | 6,668 ft |
| 1 km | 0.08 m | 0.26 ft |
| 10 km | 7.85 m | 26 ft |
| 30 km | 71 m | 232 ft |
| 50 km | 196 m | 644 ft |
| 100 km | 785 m | 2,575 ft |
| 500 km | 19,590 m | 64,272 ft |
Drop from a tangent plane, which is what the 8 inches per mile squared rule computes. Hidden height for a real observer is always less, and the calculator above uses your height to work it out.
With elevation: why the map matters
Everything on this page assumes a smooth sphere with nothing on it. The real question is almost never that. It is whether you can see a particular mountain from a particular window, and the answer depends on a ridge nobody thought about halfway along the path.
Two of the numbers above stay true in the real world: the curvature drop and the horizon over open water. The third, the hidden height, is an upper bound. Terrain closer than the target only ever takes more of it away.
That is the difference between a formula and a terrain model. UpToWhere walks the actual ground between two points on 30 m elevation data, applies the same curvature and refraction, and tells you which ridge is in the way rather than assuming there is none.
Frequently asked questions
How far can you see before the Earth curves out of view?
From standing eye level on a beach, about 4.7 km or 2.9 miles, and about 5 km with standard refraction. On a 100 m hill it is 36 km, and from the summit of Everest 336 km. The horizon distance is 3.57 times the square root of your height in metres, in kilometres.
How much curvature is in 1 mile?
About 0.2 m, or 8 inches, measured as the drop of the surface below a flat line. The rule of thumb is 8 inches times the number of miles squared, which is accurate: at 10 miles it gives 20.3 m and the exact figure is 20.33 m.
How much does the Earth curve in 100 miles?
About 2,032 m of drop from a tangent plane, or roughly 1.26 miles. How much of an object 100 miles away is actually hidden from you is a different and smaller number, because your own horizon is already tens of miles out. Enter your height in the calculator to get it.
Is the horizon 12 miles away?
Only if your eyes are about 29 m up, which is a ten-storey roof. From a beach it is under 3 miles. The 12 mile figure circulates because it is roughly right from the deck of a large ship or a cliff top.
Does this calculator include refraction?
Yes, as an option. The refraction setting uses an effective Earth radius 17% larger than the real one, the standard optical allowance, which pushes the horizon about 8% further out. There is also a 4/3 radius setting, which is the convention for radio paths.
Can I use this to check whether I can see a specific mountain?
It gives you the geometric answer, which is the ceiling. Whether you actually see it depends on the ground in between, and for that you need a terrain profile rather than a formula. That is what the map linked from this page does.
Related
Now put a real place under it
The same curvature and refraction, applied to the actual ground between two points, on 30 m elevation data. Free to try from any point on Earth.
Open the map