Distance Between Cities Calculator

Haversine Formula:

\[ d = 2r \times \arcsin\left(\sqrt{\sin^2\left(\frac{\phi_2 - \phi_1}{2}\right) + \cos\phi_1 \times \cos\phi_2 \times \sin^2\left(\frac{\lambda_2 - \lambda_1}{2}\right)}\right) \]

City 1 Latitude:

City 1 Longitude:

City 2 Latitude:

City 2 Longitude:

Distance Between Cities:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 navigation and geographical applications where precise distance measurements are needed.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2r \times \arcsin\left(\sqrt{\sin^2\left(\frac{\phi_2 - \phi_1}{2}\right) + \cos\phi_1 \times \cos\phi_2 \times \sin^2\left(\frac{\lambda_2 - \lambda_1}{2}\right)}\right) \]

Where:

\( d \) — Distance between the two points
\( r \) — Radius of the Earth (6371 km)
\( \phi_1, \phi_2 \) — Latitude of point 1 and point 2 in radians
\( \lambda_1, \lambda_2 \) — Longitude of point 1 and point 2 in radians

Explanation: The formula accounts for the curvature of the Earth to provide accurate distance measurements between any two points on the globe.

3. Importance of Accurate Distance Calculation

Details: Accurate distance calculations are crucial for navigation systems, flight planning, logistics, and geographical research. The Haversine formula provides more accurate results than simple flat-Earth approximations.

4. Using the Calculator

Tips: Enter the latitude and longitude coordinates for both cities in decimal degrees format. 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. For extreme precision, the Vincenty formula accounts for Earth's ellipsoid shape.

Q2: What's the difference between great-circle and rhumb line distance?
A: Great-circle (Haversine) is the shortest path on a sphere, while rhumb lines maintain constant bearing but are longer.

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

Q4: Why does the Earth's radius affect the calculation?
A: The formula calculates angular distance which must be converted to linear distance using the Earth's radius.

Q5: How can I find my city's coordinates?
A: Most mapping services (Google Maps, etc.) show coordinates when you right-click on a location.