Distance Between Locations Calculator

Haversine Formula:

\[ Distance = 2R \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \]

Latitude 1:

Longitude 1:

Latitude 2:

Longitude 2:

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 useful for calculating distances between geographic locations on Earth.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 2R \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \]

Where:

\( R \) — Earth's radius (6371 km)
\( \phi_1, \phi_2 \) — Latitude of point 1 and 2 in radians
\( \lambda_1, \lambda_2 \) — Longitude of point 1 and 2 in radians
\( \Delta\phi \) — Difference in latitude
\( \Delta\lambda \) — Difference in longitude

Explanation: The formula accounts for the spherical shape of the Earth, providing accurate distance calculations along the great-circle path.

3. Importance of Geographic Distance Calculation

Details: Accurate distance calculation is essential for navigation systems, logistics planning, geographic analysis, and various applications in geography, transportation, and location-based services.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Latitude ranges from -90° to 90°, longitude from -180° to 180°. Positive values for North/East, negative for South/West.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: The Haversine formula provides very accurate results for most practical purposes, with errors typically less than 0.5% for distances up to 20,000 km.

Q2: What is the difference between great-circle and rhumb line distance?
A: Great-circle distance is the shortest path between two points on a sphere, while rhumb line maintains a constant bearing. Great-circle is always shorter.

Q3: Can I use this for very short distances?
A: Yes, but for very short distances (less than 1 km), flat-earth approximations may be sufficient and computationally simpler.

Q4: Does the formula account for Earth's oblateness?
A: No, the Haversine formula assumes a perfect sphere. For higher precision, Vincenty's formulae account for Earth's ellipsoidal shape.

Q5: What coordinate format should I use?
A: Use decimal degrees format. If you have degrees-minutes-seconds, convert them to decimal degrees first.