Great Circle Calculator Geocaching

Haversine Formula:

\[ a = \sin²(\Delta\phi/2) + \cos\phi_1 \cdot \cos\phi_2 \cdot \sin²(\Delta\lambda/2) \] \[ c = 2 \cdot \text{atan2}(\sqrt{a}, \sqrt{1-a}) \] \[ d = R \cdot c \]

Latitude Point 1:

degrees

Longitude Point 1:

degrees

Latitude Point 2:

degrees

Longitude Point 2:

degrees

Unit:

Great Circle 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 geocaching and navigation applications.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ a = \sin²(\Delta\phi/2) + \cos\phi_1 \cdot \cos\phi_2 \cdot \sin²(\Delta\lambda/2) \] \[ c = 2 \cdot \text{atan2}(\sqrt{a}, \sqrt{1-a}) \] \[ d = R \cdot c \]

Where:

\( \phi \) — Latitude in radians
\( \lambda \) — Longitude in radians
\( \Delta\phi \) — Difference between latitudes
\( \Delta\lambda \) — Difference between longitudes
\( R \) — Earth's radius (6371 km)

Explanation: The formula accounts for the curvature of the Earth to calculate the shortest distance between two points on a sphere.

3. Importance of Great Circle Distance

Details: Great circle distance is crucial for geocaching, navigation, and any application requiring accurate distance measurements between geographic points.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees (e.g., 40.7128, -74.0060 for New York). Positive values 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 purposes, assuming a perfect sphere. Earth's actual shape causes minor deviations (≤0.5% error).

Q2: What coordinate format should I use?
A: Decimal degrees are recommended (e.g., 51.5074° N = 51.5074, 0.1278° W = -0.1278).

Q3: Can I use this for very short distances?
A: For distances under 1km, planar approximation might be simpler, but Haversine will still work.

Q4: Why is it called "great circle"?
A: A great circle is the largest possible circle that can be drawn on a sphere, whose plane passes through the sphere's center.

Q5: How does this help with geocaching?
A: It helps determine the exact distance between cache locations or between your current position and a cache.