# Haversine Formula

The Haversine Formula is an important mathematical tool used to measure distances on the surface of the Earth. It is mainly used in navigation and can be applied to any two points on the Earth’s surface. The Haversine Formula is based on the assumption that the Earth is a sphere, which is the most accurate model of the Earth when computing distances. The formula was developed by Edmund Halley in 17th century, and since then it has become an integral part of navigation applications.

## The Haversine Formula

Haversine Formula: a = sin²(Δφ/2) + cos φ1 . cos φ2 . sin²(Δλ/2) c = 2 * atan2( √a, √(1−a) ) d = R * c where φ is latitude, λ is longitude, Δφ is the difference in latitude, Δλ is the difference in longitude, R is the earth's radius (mean radius = 6,371km)

### Components of the Formula

Component | Description |
---|---|

a |
Square of the sine of half of the difference in latitude. |

c |
The inverse of the square root of a. |

d |
The Haversine distance. |

φ |
Latitude of a point on the Earth. |

λ |
Longitude of a point on the Earth. |

Δφ |
The difference in latitude between two points on the Earth. |

Δλ |
The difference in longitude between two points on the Earth. |

R |
The Earth’s radius (mean radius = 6,371km). |

### Uses of the Haversine Formula

The Haversine Formula is widely used in navigation applications. It can be used to calculate the distance between two points on the Earth’s surface. It is also used in aviation and marine navigation, and in calculating the amount of time needed to traverse certain distances. The Haversine Formula is also used in geographic information systems to calculate distances between two points on the Earth’s surface.

### History of the Haversine Formula

The Haversine Formula was developed by Edmund Halley in the 17th century. Halley was an astronomer, geophysicist and mathematician, and is best known for his discovery of the comet that bears his name. Halley was also the first to calculate the distance between two points on the Earth’s surface using the spherical model of the Earth. The formula was later named after him as the “Haversine Formula.”