Eratosthenes used a simple formula that relates the proportionality of the relation of the distance between two places on the meridian (d) and their difference in latitude (α) to the relation between the perimeter (P ) and the angle of the hole meridian (360º):

Earth's perimeter can therefore be calculated by the formula

We can also calculate Earth's radius using the formula

Confirm your calculations

Perimeter Calculator for Summer Solstice (June 21st)

To use the calculator to confirm your calculations fill the Distance to the Tropic of Cancer and Shadow at top fields (by this order) and then press the "Submit" button

Distance to Tropic of Cancer km
Shadow at top (in decimal degrees) º
Earth's Meridional Perimeter km
Earth's Mean Radius km

 

 

Note: 1º = 40007.86km/360º=111.1329444 km

Perimeter Calculator at Equinox (March 21st and September 23rd)

To use the calculator to confirm your calculations fill the Distance to the Equator and Shadow at top fields (by this order) and then press the "Submit" button

Distance to Equator km
Shadow at top (in decimal degrees) º
Earth's Meridional Perimeter km
Earth's Mean Radius km

 

 

Note: 1º = 40007.86km/360º=111.1329444 km