Distance Between Lat Long Calculator

Haversine Formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\phi_2-\phi_1}{2}\right) + \cos(\phi_1) \cos(\phi_2) \sin²\left(\frac{\lambda_2-\lambda_1}{2}\right)}\right) \]

Latitude 1 (φ₁):

Longitude 1 (λ₁):

Latitude 2 (φ₂):

Longitude 2 (λ₂):

Earth Radius (R):

Distance Between Points:

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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 between points on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\phi_2-\phi_1}{2}\right) + \cos(\phi_1) \cos(\phi_2) \sin²\left(\frac{\lambda_2-\lambda_1}{2}\right)}\right) \]

Where:

\( \phi_1, \lambda_1 \) — Latitude and longitude of point 1 (in radians)
\( \phi_2, \lambda_2 \) — Latitude and longitude of point 2 (in radians)
\( R \) — Radius of the Earth (default 6371 km)
\( d \) — Distance between the two points

Explanation: The formula accounts for the curvature of the Earth by using trigonometric functions to calculate the central angle between the two points.

3. Importance of Distance Calculation

Details: Accurate distance calculation between geographic coordinates is essential for navigation, geography, logistics, and many scientific 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% when calculating distances on Earth.

Q2: What's the difference between Haversine and Vincenty formulas?
A: Vincenty's formulae are more accurate (sub-millimeter precision) but more computationally intensive. Haversine is simpler and sufficient for most applications.

Q3: What is the maximum distance this can calculate?
A: The formula works for any distance, but for antipodal points (exactly opposite on the globe), numerical precision might become an issue.

Q4: Can I use this for other celestial bodies?
A: Yes, just change the radius parameter to match the body you're calculating distances on (e.g., 1737 km for the Moon).

Q5: Why does the Earth's radius matter?
A: The radius scales the angular distance (in radians) to actual distance. Using the correct radius for your planet/body is essential for accurate results.