Eratosthenes shadow calculator
Compare signed noon zenith angles at two sites and their surface separation. The result gives circumference, radius and the contribution of independent distance and angle uncertainties.
The 7.2° difference spans 800 km of surface arc. Scaling that fraction to 360° gives 40,000 km. Distance and two independent angle readings give a combined standard uncertainty of 824.49 km.
Read this calculation
C = 360° × distance / |angle A − angle B|
Observe at the same solar meridian, or correct the longitude and observation-time difference. Opposite shadow directions need opposite angle signs; two unsigned shadow lengths can hide the actual separation.
Measure a vertical stick and its shadow. Zenith angle is arctan(shadow length / stick height); note whether the Sun is north or south. Surface separation is the arc between the sites, not the distance along a winding road.