Calculate Distance Based On Coordinates

Haversine Formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{lat2-lat1}{2}\right) + \cos(lat1) \cos(lat2) \sin²\left(\frac{lon2-lon1}{2}\right)}\right) \]

Latitude 1:

Longitude 1:

Latitude 2:

Longitude 2:

Earth Radius:

Distance:

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1. What is the Haversine Formula?

The Haversine formula calculates the great-circle distance between two points on a sphere given their longitudes and latitudes. It's particularly accurate for calculating distances on Earth, accounting for the spherical shape of the planet.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{lat2-lat1}{2}\right) + \cos(lat1) \cos(lat2) \sin²\left(\frac{lon2-lon1}{2}\right)}\right) \]

Where:

\( lat1, lon1 \) — Coordinates of first point in degrees
\( lat2, lon2 \) — Coordinates of second point in degrees
\( R \) — Earth's radius (default 6371 km)

Explanation: The formula calculates the shortest distance between two points on the surface of a sphere (great-circle distance).

3. Importance of Distance Calculation

Details: Accurate distance calculation between geographic coordinates is essential for navigation, logistics, geography studies, and many location-based applications.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees (e.g., 40.7128° N, 74.0060° W as 40.7128, -74.0060). Positive values for North/East, negative for South/West.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this formula?
A: The Haversine formula is very accurate for most purposes, with errors typically less than 0.3% due to Earth's ellipsoidal shape.

Q2: What's the maximum distance this can calculate?
A: The formula works for any distance on Earth's surface, but for antipodal points (exactly opposite sides), special consideration is needed.

Q3: Why use 6371 km for Earth's radius?
A: This is the mean radius of Earth. For more precision, you could use 6378.137 km (equatorial) or 6356.752 km (polar).

Q4: Can I use this for other celestial bodies?
A: Yes, just change the radius parameter to match the body you're calculating for (e.g., 1737.4 km for the Moon).

Q5: What coordinate format should I use?
A: Decimal degrees are recommended (e.g., 34.0522° instead of 34°3'8"). The calculator automatically converts to radians.