Flat vs. Round Earth Calculator

This calculator relies on standard spherical trigonometry and optical geometry. To find the Earth's circumference using shadow lengths, the tool uses the formula earthCircum = distanceAB / (abs(shadowAngleB - shadowAngleA) / (2 * pi)), where shadow angles are derived from stick heights and shadow lengths via arctangent: shadowAngle = atan(shadowLength / stickHeight). Horizon distances and obstructed object heights are computed using the Pythagorean theorem on Earth's mean radius (approx. 6,371,000 meters), determining precisely how much of a distant structure is hidden by planetary curvature.

Let us walk through calculating shadow-based Earth circumference. Suppose two observers are separated by a distance AB of 800,000 meters (800 km). At both locations, they place vertical sticks of height 1 meter (stickHeight = 1). At location A, the measured shadow length is 0.577 meters, yielding a shadow angle of atan(0.577 / 1) = 30 degrees (0.5236 radians). At location B, the shadow length is 0.404 meters, yielding an angle of roughly 22 degrees (0.3840 radians). The absolute difference between these angles is 0.1396 radians. Dividing the separation distance (800,000 meters) by this angular fraction multiplied by 2π yields an estimated Earth circumference of approximately 40,000,000 meters, closely matching actual global measurements.

When running geodetic or horizon calculations, ensure your units remain consistent—typically converting kilometers and miles into meters for internal trigonometric accuracy. Account for atmospheric refraction when calculating precise horizon lines, as light bending can slightly extend apparent visibility ranges beyond pure geometric lines of sight. When performing shadow-based circumference experiments, ensure measurements are taken simultaneously at solar noon to minimize temporal discrepancies.