haversineképlet

The haversine formula is a mathematical formula used to calculate the great-circle distance between two points on a sphere given their longitudes and latitudes. This formula is particularly useful in navigation and cartography because it accounts for the curvature of the Earth, treating it as a perfect sphere for simplicity. The "haversine" itself refers to the haversine function, which is defined as hav(θ) = sin²(θ/2).

To apply the haversine formula, you need the latitude and longitude of the two points, typically denoted as (φ1, λ1) and (φ2, λ2). The latitudes and longitudes must be expressed in radians. The formula is then:

a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Here, Δφ is the difference in latitude (φ2 − φ1), and Δλ is the difference in longitude (λ2 − λ1). R is the Earth's radius, which can be taken as approximately 6,371 kilometers or 3,956 miles. The function atan2(y, x) calculates the arctangent of y/x, considering the signs of both arguments to determine the correct quadrant for the angle. The result 'd' is the shortest distance over the Earth's surface. The haversine formula is known for its numerical stability, especially for small distances, making it a preferred choice in many applications.