Calculate Distance By Latitude And Longitude

Haversine Formula:

\[ d = 6371 \times 2 \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta lat}{2}\right) + \cos(lat_1) \times \cos(lat_2) \times \sin^2\left(\frac{\Delta lon}{2}\right)}\right) \]

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

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 geographic coordinates on Earth.

2. How Does The Calculator Work?

The calculator uses the Haversine formula:

\[ d = 6371 \times 2 \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta lat}{2}\right) + \cos(lat_1) \times \cos(lat_2) \times \sin^2\left(\frac{\Delta lon}{2}\right)}\right) \]

Where:

\( d \) — Distance in kilometers
\( 6371 \) — Earth's radius in kilometers
\( lat_1, lat_2 \) — Latitude coordinates in radians
\( lon_1, lon_2 \) — Longitude coordinates in radians
\( \Delta lat \) — Difference in latitude (radians)
\( \Delta lon \) — Difference in longitude (radians)

Explanation: The formula accounts for the spherical shape of Earth and provides accurate distance calculations along the great-circle path.

3. Importance Of Distance Calculation

Details: Accurate distance calculation between geographic coordinates is essential for navigation systems, mapping applications, logistics planning, and geographic analysis.

4. Using The Calculator

Tips: Enter latitude values between -90° and 90°, longitude values between -180° and 180°. Use decimal degrees format for precise calculations. The calculator automatically converts degrees to radians.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: The Haversine formula provides high accuracy for most practical purposes, typically within 0.5% of the actual great-circle distance.

Q2: What is the difference between Haversine and Vincenty formulas?
A: Vincenty's formulae are more accurate and account for Earth's ellipsoidal shape, while Haversine assumes a perfect sphere. Haversine is simpler and faster.

Q3: Can I use this for very short distances?
A: Yes, but for very short distances (less than 1 km), planar distance formulas may be more appropriate and computationally efficient.

Q4: Why use 6371 km for Earth's radius?
A: 6371 km is the mean radius of Earth. For higher precision, you could use the equatorial radius (6378 km) or polar radius (6357 km).

Q5: How do I convert the result to miles?
A: Multiply the kilometer result by 0.621371 to get miles. 1 kilometer = 0.621371 miles.