Calculating Distance Between Two Locations

Haversine Formula:

\[ Distance = 6371 \times \arccos(\sin \varphi_1 \sin \varphi_2 + \cos \varphi_1 \cos \varphi_2 \cos \Delta\lambda) \]

Latitude 1 (φ1):

degrees

Longitude 1 (λ1):

degrees

Latitude 2 (φ2):

degrees

Longitude 2 (λ2):

degrees

Distance (km):

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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 locations on Earth, accounting for the planet's curvature.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 6371 \times \arccos(\sin \varphi_1 \sin \varphi_2 + \cos \varphi_1 \cos \varphi_2 \cos \Delta\lambda) \]

Where:

\( \varphi_1, \varphi_2 \) — Latitude of points 1 and 2 in radians
\( \Delta\lambda \) — Difference in longitude between two points in radians
6371 — Earth's radius in kilometers

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

3. Importance of Distance Calculation

Details: Accurate distance calculation is essential for navigation systems, logistics planning, geographic analysis, and various location-based services. The Haversine formula provides more accurate results than simple Euclidean distance for global calculations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why use Haversine instead of Euclidean distance?
A: Euclidean distance assumes a flat surface, while Haversine accounts for Earth's curvature, providing accurate results for long distances.

Q2: How accurate is the Haversine formula?
A: The formula is generally accurate to within 0.5% for most practical purposes, though it assumes a perfect sphere (Earth is slightly ellipsoidal).

Q3: What coordinate format should I use?
A: Use decimal degrees format (e.g., 40.7128° instead of 40°42'46"). Most GPS devices and mapping services provide coordinates in this format.

Q4: Can I calculate distance in miles instead of kilometers?
A: Yes, simply multiply the result by 0.621371 to convert kilometers to miles, or use Earth's radius in miles (3959) in the formula.

Q5: Are there limitations to this formula?
A: For extremely precise calculations over very long distances, more complex formulas like Vincenty's formulae may be needed to account for Earth's ellipsoidal shape.