The haversine formula calculates the shortest distance between two points, whose latitudes and longitudes are known, in a sphere. When used for points on the Earth, the calculated distance is approximate as the formula assumes the Earth to be a perfect sphere.
The haversine formula can be expressed as follows:
The central angle haversine can be computed as follows:
The values in the formula above stand for the following:
We can derive the haversine formula to calculate the distance d between two points as follows:
a = sin²(Δlat/2) + cos(lat1).cos(lt2).sin²(Δlong/2)
c = 2.atan2(√a, √(1−a))
d = R.c
In the formula above, the values are calculated as follows:
Δlat = lat1 − lat2
Δlong = long1 − long2
R
is the radius of the earth, that is, 6,371 kilometers.import math def haversine_distance(coord1: tuple, coord2: tuple): lon1, lat1 = coord1 lon2, lat2 = coord2 R = 6371000 phi_1 = math.radians(lat1) phi_2 = math.radians(lat2) delta_phi = math.radians(lat2 - lat1) delta_lambda = math.radians(lon2 - lon1) a = math.sin(delta_phi / 2.0) ** 2 + math.cos(phi_1) * math.cos(phi_2) * math.sin(delta_lambda / 2.0) ** 2 c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a)) meters = R * c km = meters / 1000.0 meters = round(meters, 3) km = round(km, 3) miles = km * 0.621371 print(f"Distance: {meters} m") print(f"Distance: {km} km") print(f"Distance: {miles} miles") if __name__ == "__main__": lat1 = 43.2341 lon1 = 0.5463 lat2 = 58.1234 lon2 = 88.9421 coord1 = (lat1, lon1) coord2 = (lat2, lon2) print("Distance between", coord1, "and" , coord2, ":") haversine_distance(coord1, coord2)
haversine_distance()
method is invoked to find the haversine distance.RELATED TAGS
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