Earth Curvature Calculator
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Other tools you may find usefulEarth's curvature calculator - horizon drop and hidden height
Calculate how much the Earth's surface curves at a given distance. Enter the distance in kilometers or meters and the calculator will provide the fall of the horizon in meters and the height of objects hidden behind the curve. An ideal tool for visualization, surveying, photography and physics learning.
Run the curvature calculator See the formulas
What does the calculator calculate
- Horizon drop- how much the Earth's surface falls at a given distance.
- Hidden Object Height– how much of a tower, mountain or building is hidden behind the curve.
- Visibility distance– how far the horizon extends from a given viewing height.
- Comparisons at different radii– ability to modify the value of the Earth's radius.
Formulas used in calculations
R = 6,371,000 m (average radius of the Earth)
drop ≈ d² / (2R)
exactly: drop = R - √(R² - d²)
horizon: D = √(2Rh)For most distances up to several dozen kilometers, the approximate formula is sufficient. The valuedrop_exactapplies the full geometric pattern. The calculator shows both versions, making it easy to compare the difference between them.
Step-by-step instructions
- Enter the distance from the observation point to the target in kilometers or meters.
- Optionally, enter the observer's height above ground level to account for the visibility of the horizon.
- ClickCalculate. The tool will provide the horizon drop and hidden height.
- Compare results at different distances - see how quickly the curvature effect increases.
Calculation examples
Distance 10 km
drop ≈ 7.8 m. This means that the surface drops by almost 8 meters relative to the tangent line.
Distance 50 km
drop ≈ 196 m. In practice, this means that an object standing at sea level is almost completely hidden.
Distance 100 km
drop ≈ 785 m. At such distances, visibility limits the horizon even at high observation altitudes.
Observer at an altitude of 100 m
Horizon range D ≈ 35.7 km. Further on, the objects disappear behind the curve.
Practical applications
Geodesy
Correction of measurements at large distances, determining visibility between measurement points, taking into account atmospheric refraction.
Landscape photography
Planning long-range photos - determining whether a particular peak or tower will be visible from beyond the horizon.
Astronomical Observations
Calculate the height at which the Moon or Sun appears above the local horizon and correct for low angles.
Education
Showing in a simple way that the Earth's surface is curved, and how a small effect becomes noticeable at large distances.
FAQ
How accurate is the calculator?
Accuracy depends on distance. For distances below 100 km, the error between the approximate and exact formula does not exceed 1%. The exact version uses full spherical geometry.
Is atmospheric refraction taken into account?
No. In the basic mode, a perfect sphere without refraction is assumed. In practice, refraction slightly "raises" the horizon, which can be estimated by multiplying the result by 0.85.
How to change the radius of the Earth?
The default is 6,371 km. You can enter your own value for the ellipsoid or planet to simulate other worlds.
Why isn't the result linear?
The curvature increases with the square of the distance - by doubling the distance, the slope quadruples.
Approximate values of horizon drop
| Distance [km] | Drop [m] |
|---|---|
| 1 | 0.08 |
| 5 | 1.96 |
| 10 | 7.8 |
| 25 | 49 |
| 50 | 196 |
| 100 | 785 |
Summary:Earth's curvature is a geometric phenomenon visible on long distances. This calculator allows you to instantly calculate the fall of the horizon and understand why objects disappear behind the sea line or mountain horizon.