Calculate Distance In Miles

Haversine Formula:

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

Point 1 Latitude:

Point 1 Longitude:

Point 2 Latitude:

Point 2 Longitude:

Distance (miles):

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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 on Earth, accounting for the planet's curvature.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

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

Where:

\( d \) — Distance in miles
\( r \) — Earth's radius (3958.8 miles)
\( \phi_1, \phi_2 \) — Latitude of point 1 and point 2 in radians
\( \lambda_1, \lambda_2 \) — Longitude of point 1 and point 2 in radians
\( \Delta\phi \) — Difference in latitudes
\( \Delta\lambda \) — Difference in longitudes

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 crucial for navigation, logistics, geography studies, and various applications in transportation, mapping, and location-based services.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees format. Latitude ranges from -90° to 90° (negative for Southern Hemisphere), longitude ranges from -180° to 180° (negative for Western Hemisphere).

5. Frequently Asked Questions (FAQ)

Q1: Why use Haversine instead of simple Euclidean distance?
A: Haversine accounts for Earth's curvature, providing accurate great-circle distances, while Euclidean distance assumes a flat surface and is only accurate for very short distances.

Q2: How accurate is this calculation?
A: The Haversine formula is very accurate for most practical purposes, typically within 0.5% of the actual great-circle distance.

Q3: Can I use this for air or sea navigation?
A: Yes, this calculates the great-circle distance which is the shortest path between two points on a sphere, commonly used in aviation and maritime navigation.

Q4: What's the maximum distance this can calculate?
A: The formula works for any two points on Earth, from a few feet to the maximum possible Earth surface distance (approximately 12,450 miles).

Q5: Why are the results in miles?
A: This calculator uses Earth's radius in miles. For kilometers, you would use Earth's radius as 6371 km in the formula.