Flying Distance Calculator Between Cities

Haversine Formula:

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

City 1 Latitude:

City 1 Longitude:

City 2 Latitude:

City 2 Longitude:

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 useful for calculating the shortest distance between two locations on the Earth's surface.

2. How Does The Calculator Work?

The calculator uses the Haversine formula:

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

Where:

\( d \) — Distance between two points
\( r \) — Earth's radius (6371 km)
\( \phi_1, \phi_2 \) — Latitudes of point 1 and point 2 in radians
\( \lambda_1, \lambda_2 \) — Longitudes of point 1 and point 2 in radians
\( \Delta\phi \) — Difference between latitudes
\( \Delta\lambda \) — Difference between longitudes

Explanation: The formula accounts for the spherical shape of the Earth, providing the shortest path (great-circle) between two points.

3. Importance Of Great-Circle Distance

Details: Great-circle distance is crucial for aviation, navigation, and logistics as it represents the shortest path between two points on a sphere, saving time and fuel in transportation.

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: What Is The Difference Between Great-Circle And Rhumb Line Distance?
A: Great-circle is the shortest path on a sphere, while rhumb line maintains constant bearing. Great-circle is shorter but requires course changes.

Q2: How Accurate Is The Haversine Formula?
A: Very accurate for most practical purposes, assuming a spherical Earth. For extreme precision, ellipsoidal models like Vincenty's formulae are used.

Q3: Can I Use This For Any Two Locations Worldwide?
A: Yes, the formula works for any two points on Earth as long as valid coordinates are provided.

Q4: Why Use 6371 km As Earth's Radius?
A: This is the mean radius of Earth. For more precision, you could use equatorial (6378 km) or polar (6357 km) radius depending on location.

Q5: How Do I Convert DMS To Decimal Degrees?
A: Decimal degrees = degrees + minutes/60 + seconds/3600. For example, 40°45'30" = 40 + 45/60 + 30/3600 = 40.7583°.