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 21^{st})

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 21^{st} and September 23^{rd})

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 |