Earth curvature calculator
“If Earth were a ball, objects would vanish over the horizon” — and they do. Enter a distance and your eye height and see how much of a target the curvature hides.
You can see a bridge or a far shore over a dozen kilometres away, so there is no curvature — Earth must be flat.
On a 6,371 km sphere the bottom of a distant object hides behind the bulge, yet a tall observer or a tall target still sees the upper part. The calculator below shows exactly how much should disappear — and it matches observation.
The most common error in curvature debates is the “8 inches per mile squared” formula. It describes the drop of the curve below a tangent line, not how much of an object actually hides. Real visibility also depends on your eye height: the higher you look, the farther the horizon and the less of the target is hidden.
That is why almost nothing vanishes from a beach, while more disappears from a tall dune. The same object “rises” out of the horizon when you raise your viewpoint — something a flat map cannot explain.
Set the distance, your eye height, and the target height. The refraction toggle adds the typical bending of light rays in the atmosphere.
Your observation
- Your horizon
- 4.7 km
- Hidden by curvature
- 18.5 m
- Visible top of the target
- 11.5 m
- Naïve “8 inches per mile²”
- 31.4 m
The model assumes a 6,371 km sphere and ignores waves, terrain, and variable refraction. Refraction is modelled as inflating the effective radius by a factor of 7/6.
- The naïve “8 inches per mile²” always overstates hiding because it ignores the observer's height.
- Raising your eyes reveals the lower parts of an object — direct evidence of curvature.
- Atmospheric refraction shifts the result but does not remove the global bottom-first vanishing pattern.
Earth curvature — questions
The drop of the curve below a tangent line is about 0.0785 metres over the first kilometre and grows with the square of distance (about 7.8 m over 10 km). That is not the object's “hidden” amount, though — that is found by accounting for the observer's height and the horizon.
It gives the drop of the curve below a tangent drawn from ground level, not the real hiding seen by an observer with a non-zero eye height. In practice less disappears, because your line of sight reaches the horizon first and only beyond it does the object start to hide.
Refraction bends rays slightly downward, so you see a little farther than pure geometry predicts. It is usually modelled as inflating the radius by a factor of 7/6. That shifts the numbers but does not remove the bottom-first vanishing of objects.
At an eye height of about 1.7 m the horizon is roughly 4.7 km away. From a 100 m tower it is about 36 km, and from an airliner's cruising altitude (11 km) over 370 km. This growth of range with height is exactly what a globe predicts.