Haversine Formula in Python

23 Haversine

Haversine Formula

The Haversine formula calculates the distance between two points on the Earth's surface taking into account its spherical shape.

Key Points

The Earth is approximately spherical.
The formula computes the great-circle distance — the shortest path between two points on a sphere.
Latitude and longitude coordinates are used.

Formulas

R = 6371 km (Earth's radius)
Δlat = lat2 - lat1
Δlon = lon2 - lon1
a = sin²(Δlat/2) + cos(lat1) * cos(lat2) * sin²(Δlon/2)
c = 2 * arctan2(√a, √(1-a))
d = R * c

Python Example

import math

def haversine(lat1, lon1, lat2, lon2):
    R = 6371  # Earth's radius in kilometers
    # Convert degrees to radians
    lat1, lon1, lat2, lon2 = map(math.radians, [lat1, lon1, lat2, lon2])

    dlat = lat2 - lat1
    dlon = lon2 - lon1

    a = math.sin(dlat / 2) ** 2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlon / 2) ** 2
    c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))

    distance = R * c
    return distance


# Example usage:
berlin = (52.52, 13.4)
paris = (48.85, 2.35)

dist = haversine(berlin[0], berlin[1], paris[0], paris[1])
print(f"Distance between Berlin and Paris: {dist:.2f} km")

# Distance between Berlin and Paris: 877.68 km