Distance Between Cities Calculator

Haversine Formula:

\[ Distance = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\Delta lat}{2}\right) + \cos(lat_1) \cos(lat_2) \sin²\left(\frac{\Delta lon}{2}\right)}\right) \]

Latitude City 1:

degrees

Longitude City 1:

degrees

Latitude City 2:

degrees

Longitude City 2:

degrees

Distance Between Cities:

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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 Earth's spherical shape.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\Delta lat}{2}\right) + \cos(lat_1) \cos(lat_2) \sin²\left(\frac{\Delta lon}{2}\right)}\right) \]

Where:

\( R \) — Earth's radius (6371 km)
\( lat_1, lat_2 \) — Latitudes of two points in radians
\( lon_1, lon_2 \) — Longitudes of two points in radians
\( \Delta lat \) — Difference in latitude
\( \Delta lon \) — 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 navigation, logistics, travel planning, and geographical analysis. The Haversine formula provides more accurate results than simple Euclidean distance for spherical surfaces.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why use Haversine instead of Euclidean distance?
A: Euclidean distance assumes a flat surface, while Haversine accounts for Earth's curvature, providing accurate great-circle distances.

Q2: How accurate is this calculation?
A: The Haversine formula is accurate to within 0.5% for most practical purposes, assuming a spherical Earth model.

Q3: What coordinate format should I use?
A: Use decimal degrees (e.g., 40.7128°N, 74.0060°W). If you have degrees-minutes-seconds, convert to decimal first.

Q4: Does this account for elevation differences?
A: No, this calculates surface distance only. For precise measurements involving significant elevation changes, additional calculations are needed.

Q5: Can I use this for very long distances?
A: Yes, the Haversine formula works well for any distance on Earth's surface, from a few meters to the maximum possible (approximately 20,000 km).