Calculate Distance Between Lat Long

Haversine Formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\varphi_2-\varphi_1}{2}\right) + \cos(\varphi_1) \cos(\varphi_2) \sin²\left(\frac{\lambda_2-\lambda_1}{2}\right)}\right) \]

Latitude 1 (φ₁):

Longitude 1 (λ₁):

Latitude 2 (φ₂):

Longitude 2 (λ₂):

Unit:

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 between points on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\varphi_2-\varphi_1}{2}\right) + \cos(\varphi_1) \cos(\varphi_2) \sin²\left(\frac{\lambda_2-\lambda_1}{2}\right)}\right) \]

Where:

\( \varphi_1, \lambda_1 \) — Latitude and longitude of point 1 (in radians)
\( \varphi_2, \lambda_2 \) — Latitude and longitude of point 2 (in radians)
\( R \) — Earth's radius (6371 km or 3959 miles)
\( d \) — Distance between the two points

Explanation: The formula accounts for the spherical shape of the Earth, providing more accurate results than simple planar geometry calculations.

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). Latitude must be between -90° and 90°, longitude between -180° and 180°.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculation?
A: The Haversine formula is accurate to about 0.3% for most Earth distances, assuming a perfect sphere (Earth is actually an oblate spheroid).

Q2: What's the difference between great-circle and rhumb line distance?
A: Great-circle is the shortest path between points on a sphere (what we calculate), while rhumb line maintains constant bearing (longer but easier to navigate).

Q3: Can I use this for very short distances?
A: For distances under 20 km, planar approximation might be sufficient, but Haversine will still give more accurate results.

Q4: Why does the Earth's radius matter?
A: The radius scales the angular distance to actual distance. Using 6371 km gives distance in kilometers, 3959 miles gives miles.

Q5: Are there more accurate formulas?
A: Vincenty's formulae account for Earth's ellipsoidal shape and are more accurate, but more computationally intensive.