Haversine Distance Calculator

Haversine Formula:

\[ d = 2 \times R \times \arcsin\left(\sqrt{\sin²\left(\frac{lat2 - lat1}{2}\right) + \cos(lat1) \times \cos(lat2) \times \sin²\left(\frac{lon2 - lon1}{2}\right)}\right) \]

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

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:

\[ d = 2 \times R \times \arcsin\left(\sqrt{\sin²\left(\frac{lat2 - lat1}{2}\right) + \cos(lat1) \times \cos(lat2) \times \sin²\left(\frac{lon2 - lon1}{2}\right)}\right) \]

Where:

\( d \) — Distance in kilometers
\( R \) — Earth's radius (6371 km)
\( lat1, lat2 \) — Latitude of points 1 and 2 (in radians)
\( lon1, lon2 \) — Longitude of points 1 and 2 (in radians)

Explanation: The formula accounts for the curvature of the Earth by using trigonometric functions to calculate the shortest path between two points on a sphere.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for navigation systems, flight planning, geographical analysis, and many location-based services. The Haversine formula provides a good balance between accuracy and computational simplicity.

4. Using the Calculator

Tips: Enter the latitude and longitude for both points in decimal degrees format (e.g., 40.7128 for New York). Positive values are for North/East, negative for South/West.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: It's very accurate for most practical purposes, with errors typically less than 0.3% when calculating distances on Earth.

Q2: What's the maximum distance this can calculate?
A: The formula works for any distance on a sphere, but for antipodal points (exactly opposite sides of Earth), special consideration is needed.

Q3: Can I use this for driving distances?
A: This calculates straight-line (great-circle) distances. Driving distances will typically be longer due to roads and terrain.

Q4: What coordinate system should I use?
A: Use decimal degrees in WGS84 format (same as most GPS devices). For other formats, convert to decimal degrees first.

Q5: Why not use simple Pythagorean theorem?
A: On a spherical Earth, Pythagorean theorem becomes increasingly inaccurate with distance. Haversine accounts for Earth's curvature.