Air Distance Between Cities Calculator

Great-circle Distance Formula:

\[ Distance = 6371 \times 2 \times \arcsin\left(\sqrt{\sin^2(\Delta lat/2) + \cos(lat1)\cos(lat2)\sin^2(\Delta lon/2)}\right) \]

Latitude City 1:

degrees

Longitude City 1:

degrees

Latitude City 2:

degrees

Longitude City 2:

degrees

Air 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, measured along the surface. For Earth, this represents the shortest air distance between two locations.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 6371 \times 2 \times \arcsin\left(\sqrt{\sin^2(\Delta lat/2) + \cos(lat1)\cos(lat2)\sin^2(\Delta lon/2)}\right) \]

Where:

\( 6371 \) — Earth's radius in kilometers
\( lat1, lat2 \) — Latitude coordinates in radians
\( lon1, lon2 \) — Longitude coordinates in radians
\( \Delta lat \) — Difference in latitude
\( \Delta lon \) — Difference in longitude

Explanation: The formula calculates the central angle between two points and converts it to distance using Earth's radius.

3. Importance of Air Distance Calculation

Details: Great-circle distance is essential for aviation, navigation, logistics planning, and understanding the true shortest path between locations on Earth's surface.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Valid ranges: latitude -90° to 90°, longitude -180° to 180°. Positive values for North/East, negative for South/West.

5. Frequently Asked Questions (FAQ)

Q1: Why use great-circle distance instead of straight line?
A: Great-circle distance follows Earth's curvature, providing the actual shortest path between two points on a sphere, unlike a straight line through Earth.

Q2: How accurate is this calculation?
A: The calculation assumes a perfect sphere with radius 6371 km. Actual Earth is slightly ellipsoidal, but the difference is typically less than 0.5%.

Q3: Can I use this for driving distance?
A: No, this calculates air distance. Driving distance is longer due to roads, terrain, and infrastructure constraints.

Q4: What coordinate format should I use?
A: Use decimal degrees (e.g., 40.7128° for New York). For DMS coordinates, convert to decimal first.

Q5: Does this account for altitude differences?
A: No, the calculation is for surface distance only. Altitude differences have negligible effect on long-distance calculations.