# Earth Curvature Calculator

Accurately calculate the curvature you are supposed to see on the ball Earth.

Distance | Curvature |
---|---|

1 km | 0.00008 km = 0.08 meters |

2 km | 0.00031 km = 0.31 meters |

5 km | 0.00196 km = 1.96 meters |

10 km | 0.00785 km = 7.85 meters |

20 km | 0.03139 km = 31.39 meters |

50 km | 0.19620 km = 196.20 meters |

100 km | 0.78479 km = 784.79 meters |

200 km | 3.13897 km = 3138.97 meters |

500 km | 19.6101 km = 19610.09 meters |

1000 km | 78.3196 km = 78319.62 meters |

Distance | Curvature |
---|---|

1 mile | 0.00013 miles = 0.67 feet |

2 miles | 0.00051 miles = 2.67 feet |

5 miles | 0.00316 miles = 16.67 feet |

10 miles | 0.01263 miles = 66.69 feet |

20 miles | 0.05052 miles = 266.75 feet |

50 miles | 0.31575 miles = 1667.17 feet |

100 miles | 1.26296 miles = 6668.41 feet |

200 miles | 5.05102 miles = 26669.37 feet |

500 miles | 31.5336 miles = 166497.53 feet |

1000 miles | 125.632 miles = 663337.65 feet |

## Explanation:

The Earth's radius `(r)`

is 6371 km or 3959 miles, based on numbers from Wikipedia,

which gives a circumference `(c)`

of
`c = 2 * π * r = 40 030 km`

We wish to find the height `(h)`

which is the drop in curvature over the distance `(d)`

Using the circumference we find that 1 kilometer has the angle`360° / 40 030 km = 0.009°`

. The angle `(a)`

is then `a = 0.009° * distance (d)`

The derived formula `h = r * (1 - cos a)`

is accurate for any distance `(d)`