City To City Distance Calculator

Haversine Formula:

\[ Distance = 2R \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \]

City 1 Latitude:

degrees

City 1 Longitude:

degrees

City 2 Latitude:

degrees

City 2 Longitude:

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 useful for calculating distances between cities on Earth, accounting for the planet's curvature.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 2R \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \]

Where:

\( R \) — Earth's radius (6371 km)
\( \phi_1, \phi_2 \) — Latitudes of point 1 and point 2
\( \lambda_1, \lambda_2 \) — Longitudes of point 1 and point 2
\( \Delta\phi \) — Difference in latitude
\( \Delta\lambda \) — Difference in longitude

Explanation: The formula calculates the shortest distance between two points on the surface of a sphere, following the great-circle path.

3. Importance of Distance Calculation

Details: Accurate distance calculation between cities is essential for travel planning, logistics, navigation systems, geographic analysis, and various scientific applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: The formula assumes Earth is a perfect sphere, providing accuracy within 0.5% for most practical purposes. For higher precision, ellipsoidal models are used.

Q2: What's the difference between great-circle and rhumb line distance?
A: Great-circle is the shortest path between two points on a sphere, while rhumb line maintains constant bearing. Great-circle is always shorter.

Q3: Can I use this for very short distances?
A: Yes, but for distances under 1 km, flat-earth approximations may be sufficiently accurate and computationally simpler.

Q4: How do I find coordinates for cities?
A: Use online geocoding services, GPS devices, or mapping applications to obtain precise latitude and longitude coordinates.

Q5: Why use kilometers instead of miles?
A: The calculator uses kilometers as the standard metric unit. To convert to miles, multiply the result by 0.621371.