Haversine Distance Calculator

Formula

\[ d = 2 \times r \times \arcsin \left( \sqrt{\sin^2 \left( \frac{\Delta \text{lat}}{2} \right) + \cos(\text{lat}_1) \times \cos(\text{lat}_2) \times \sin^2 \left( \frac{\Delta \text{lon}}{2} \right)} \right) \]

Where:

\( d \) is the Haversine distance between the two points (km)
\( r \) is the radius of the sphere (typically 6371 km for Earth)
\( \text{lat}_1 \), \( \text{lon}_1 \) are the latitude and longitude of the first point (degrees)
\( \text{lat}_2 \), \( \text{lon}_2 \) are the latitude and longitude of the second point (degrees)

What is Haversine Distance?

The Haversine distance is a method of calculating the shortest distance between two points on the surface of a sphere, given their latitudes and longitudes. This calculation accounts for the Earth's curvature and provides more accurate results compared to planar distance calculations. It is commonly used in navigation and geographic information systems.

Examples

Example 1:

Point 1: Latitude 52.2296756, Longitude 21.0122287
Point 2: Latitude 41.8919300, Longitude 12.5113300
Radius of Earth: 6371 km
Haversine Distance: \[ 2 \times 6371 \times \arcsin \left( \sqrt{\sin^2 \left( \frac{10.338}{2} \right) + \cos(0.911) \times \cos(0.732) \times \sin^2 \left( \frac{9.978}{2} \right)} \right) \approx 1318.68 \text{ km} \]

Example 2:

Point 1: Latitude 34.052235, Longitude -118.243683
Point 2: Latitude 40.712776, Longitude -74.005974
Radius of Earth: 6371 km
Haversine Distance: \[ 2 \times 6371 \times \arcsin \left( \sqrt{\sin^2 \left( \frac{0.115}{2} \right) + \cos(0.595) \times \cos(0.710) \times \sin^2 \left( \frac{0.125}{2} \right)} \right) \approx 3944.98 \text{ km} \]