Distance Calculator

Haversine Formula:

\[ d = 2r \times \arcsin\left(\sqrt{\sin^2\left(\frac{\phi_2 - \phi_1}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\lambda_2 - \lambda_1}{2}\right)}\right) \]

Latitude Point 1:

Longitude Point 1:

Latitude Point 2:

Longitude Point 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 important for navigation and geographical applications where precise distance measurements are needed.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2r \times \arcsin\left(\sqrt{\sin^2\left(\frac{\phi_2 - \phi_1}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\lambda_2 - \lambda_1}{2}\right)}\right) \]

Where:

\( d \) — Distance between the two points
\( r \) — Radius of the Earth (6371 km)
\( \phi_1, \phi_2 \) — Latitude of point 1 and point 2
\( \lambda_1, \lambda_2 \) — Longitude of point 1 and point 2

Explanation: The formula accounts for the curvature of the Earth to provide accurate distance measurements between any two points on the globe.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for navigation systems, logistics planning, geographical analysis, and many scientific applications.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees format (e.g., 40.7128, -74.0060 for New York). Latitude ranges from -90 to 90, longitude from -180 to 180.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between Haversine and Vincenty formulas?
A: Vincenty's formulae are more accurate as they account for Earth's ellipsoidal shape, but are more computationally intensive.

Q3: Can I use this for short distances?
A: Yes, though for very short distances (under 1km), Euclidean distance might be sufficient.

Q4: Why does the Earth's radius affect the calculation?
A: The formula calculates angular distance which must be converted to linear distance using the sphere's radius.

Q5: How do I convert DMS to decimal degrees?
A: Decimal degrees = degrees + (minutes/60) + (seconds/3600). South/West coordinates are negative.