Great Circle Distance Calculator

Great Circle Distance Formula:

\[ \text{distance} = r \times \arccos(\sin(lat_1) \times \sin(lat_2) + \cos(lat_1) \times \cos(lat_2) \times \cos(\Delta lon)) \]

Earth Radius:

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

Great Circle Distance:

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1. What is Great Circle Distance?

The Great Circle Distance is the shortest distance between two points on the surface of a sphere. For Earth, it represents the shortest path between two locations (as the crow flies).

2. How Does the Calculator Work?

The calculator uses the Great Circle Distance formula:

\[ \text{distance} = r \times \arccos(\sin(lat_1) \times \sin(lat_2) + \cos(lat_1) \times \cos(lat_2) \times \cos(\Delta lon)) \]

Where:

\( r \) — Radius of the sphere (Earth's radius is approximately 6,371 km)
\( lat_1, lat_2 \) — Latitude of points 1 and 2 in radians
\( \Delta lon \) — Difference in longitude between the two points in radians

Explanation: The formula calculates the central angle between two points and multiplies it by the sphere's radius to get the distance.

3. Importance of Great Circle Distance

Details: Great circle distances are crucial for navigation, flight planning, telecommunications, and any application requiring accurate distance measurements on a spherical surface.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees (e.g., 40.7128 for New York City). Positive values for North/East, negative for South/West. Default Earth radius is 6,371 km.

5. Frequently Asked Questions (FAQ)

Q1: Why not use simple Euclidean distance?
A: Euclidean distance works for flat surfaces but becomes increasingly inaccurate for large distances on a sphere.

Q2: How accurate is this calculation?
A: It's mathematically exact for a perfect sphere. Earth's actual shape (oblate spheroid) may introduce minor errors (~0.3%).

Q3: Can I use this for other planets?
A: Yes, just input the appropriate radius for the celestial body you're calculating for.

Q4: What's the maximum distance this can calculate?
A: Theoretically up to half the circumference of the sphere (πr), but practical limits depend on coordinate precision.

Q5: How does this differ from Haversine formula?
A: Both calculate great circle distance, but Haversine is more numerically stable for very small distances.