Flat vs Round Earth Calculator

This calculator compares two idealized geometric models over a chosen surface distance. In the flat baseline, a perfectly level surface has no curvature drop, so its value remains zero regardless of distance. In the spherical model, the surface continually turns away from the tangent line. The calculator uses a mean Earth radius of 6,371 kilometers and evaluates the exact circular relationship rather than relying only on a short-distance rule of thumb. Curvature drop here means the vertical separation between the tangent at the starting point and the circular surface after traveling the entered arc distance. The central angle equals arc distance divided by Earth radius, and the drop equals radius multiplied by one minus the cosine of that angle. For short distances this closely matches distance squared divided by twice the radius. The difference grows approximately with the square of distance, which is why it is small across a field but substantial across tens or hundreds of kilometers. Observer height is used separately to find the geometric horizon. The straight-line horizon distance follows from a right triangle whose sides include Earth radius and Earth radius plus observer height. This is a vacuum geometry result. Atmospheric refraction commonly bends light downward and can make the visible horizon farther away, while terrain, waves, buildings, vegetation, and instrument height can obstruct it. The curvature-drop number is also not automatically the amount of a distant object hidden from a particular observer; that requires a complete line-of-sight calculation using both endpoint heights. The comparison is useful for surveying lessons, photography planning, radio-path intuition, and checking common curvature approximations. It is not a geodetic survey model. Earth is an oblate ellipsoid rather than a perfect sphere, elevations vary, and local gravity does not define a single universal visual level over long paths. For precise engineering or navigation, use an ellipsoidal Earth model, surveyed coordinates, atmospheric assumptions, and terrain data. This tool instead provides a transparent, reproducible comparison that makes the mathematical consequence of curvature easy to inspect.