Earth radius from horizon dip
Use eye height and the angle below a level horizontal to infer the spherical radius. Enter the measurement uncertainties to see how strongly a small dip error changes the answer.
A 0.321° geometric dip from 100 m implies radius 6,371.762 km. Independent height and angle uncertainties combine to 208.476 km; the angle enters nonlinearly, so a small dip error can dominate.
Read this calculation
R = h / (sec δ − 1)
The tangent from the observer meets the spherical surface at a right angle. Its triangle gives cos(dip) = R / (R + height). Solving for R turns the measured angle into a radius.
Use a level reference and an unobstructed smooth horizon. Correct a refracted apparent dip before entering the geometric angle. A shared calibration bias does not disappear by repeating the same measurement.