Distance Between 2 Cities Calculator

Great-circle Distance Formula:

\[ Distance = 6371 \times \arccos(\sin(lat_1) \sin(lat_2) + \cos(lat_1) \cos(lat_2) \cos(\Delta lon)) \]

City 1 Latitude:

degrees

City 1 Longitude:

degrees

City 2 Latitude:

degrees

City 2 Longitude:

degrees

Distance Between Cities:

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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 of the sphere. For Earth, this represents the shortest path between two locations, commonly used in aviation and navigation.

2. How Does the Calculator Work?

The calculator uses the great-circle distance formula:

\[ Distance = 6371 \times \arccos(\sin(lat_1) \sin(lat_2) + \cos(lat_1) \cos(lat_2) \cos(\Delta lon)) \]

Where:

\( Distance \) — Great-circle distance in kilometers
\( 6371 \) — Earth's mean radius in kilometers
\( lat_1, lat_2 \) — Latitudes of the two cities in radians
\( \Delta lon \) — Difference in longitude between the two cities in radians
\( \arccos \) — Inverse cosine function

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

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for navigation, flight planning, logistics, transportation, and geographical analysis. It helps determine optimal routes and travel times.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Latitude ranges from -90° (South) to 90° (North), longitude from -180° (West) to 180° (East). Ensure coordinates are valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why use great-circle distance instead of straight line?
A: Great-circle distance accounts for Earth's curvature, providing the actual shortest path on the spherical surface, unlike straight-line distance through the Earth.

Q2: How accurate is this calculation?
A: The calculation assumes a perfect sphere with radius 6371 km. For higher precision, Earth's ellipsoidal shape should be considered, but this provides excellent accuracy for most applications.

Q3: Can I use this for any two points on Earth?
A: Yes, the formula works for any two points on Earth's surface, as long as valid coordinates are provided.

Q4: What's the difference between this and driving distance?
A: Great-circle distance is the "as the crow flies" shortest path. Driving distance accounts for roads, terrain, and infrastructure, and is always longer.

Q5: How do I find coordinates for my cities?
A: Use GPS devices, online maps (Google Maps, etc.), or geographic databases. Right-click on locations in most mapping services to get coordinates.