How to Calculate Distance between Geodetic Coordinates using Haversine Formula | d = R × c

Описание: HAVERSINE FORMULA
What is the Haversine Formula?
The Haversine formula calculates the great-circle distance between two points on the surface of a sphere (e.g., the Earth) given their latitude and longitude. It accounts for the Earth's curvature and is widely used for distance calculations in navigation, geography, and mapping.
The haversine formula is a very accurate way of computing distances between two points on the surface of a sphere using the latitude and longitude of the two points.
a = sin²(φB - φA/2) + cos φA * cos φB * sin²(λB - λA/2)
c = 2 * atan2( √a, √(1−a) )
d = R ⋅ c
From the above equation
• φ is latitude,
• λ is longitude,
• R is earth’s radius (mean radius = 6,371km)
Step-by-Step Instructions
1. Convert Degrees to Radians:
2. Plug in the Values: Substitute the latitude (φ) and longitude (λ) differences into the formula.
3. Perform the Calculations:
• Compute a first.
• Use a to find c.
• Multiply c by the Earth's radius R to get d.

Why is it Used?
1. Accuracy: It provides a reasonably accurate distance over the Earth's surface, especially for shorter distances (up to 1,000 km).
2. Simplicity: The formula is computationally efficient, making it suitable for navigation and GPS applications.
3. Curved Surface: Unlike planar distance formulas, it accounts for Earth's curvature, providing a realistic measure of distance.
When is it Used?
1. Navigation: To determine the shortest path between two locations, such as for flights or maritime routes.
2. Geospatial Applications: For analyzing spatial data, e.g., proximity queries in GIS.
3. Travel Distance Estimation: For mapping services, like Google Maps, to compute approximate distances.
4. Small to Medium Distances: When high-precision geodesic distances (e.g., with ellipsoidal models) are not required.
When Not to Use It:
• For very long distances (e.g., intercontinental) or high-precision requirements, as the Earth's ellipsoidal shape can lead to minor inaccuracies.
• For local distances, where planar distance formulas may suffice.