Calculate Distance From Longitude Latitude

Haversine Formula:

\[ Distance = 6371 \times 2 \times \arcsin\left(\sqrt{\sin²\left(\frac{\Delta lat}{2}\right) + \cos(lat1) \cos(lat2) \sin²\left(\frac{\Delta lon}{2}\right)}\right) \text{ km} \]

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 locations on Earth, accounting for the Earth's spherical shape.

2. How Does The Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 6371 \times 2 \times \arcsin\left(\sqrt{\sin²\left(\frac{\Delta lat}{2}\right) + \cos(lat1) \cos(lat2) \sin²\left(\frac{\Delta lon}{2}\right)}\right) \text{ km} \]

Where:

\( lat1, lat2 \) — Latitude coordinates in degrees
\( lon1, lon2 \) — Longitude coordinates in degrees
\( \Delta lat \) — Difference in latitude (radians)
\( \Delta lon \) — Difference in longitude (radians)
6371 — Earth's radius in kilometers

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 is crucial for navigation, geography, logistics, travel planning, and various scientific applications where precise measurements between geographic coordinates are required.

4. Using The Calculator

Tips: Enter latitude values between -90° and 90°, longitude values between -180° and 180°. Use decimal degrees for precise calculations. All values must be within valid geographic ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is a great-circle distance?
A: The shortest distance between two points on the surface of a sphere, measured along the surface rather than through the sphere.

Q2: How accurate is the Haversine formula?
A: It's very accurate for most practical purposes, assuming a spherical Earth. For extreme precision, ellipsoidal models like Vincenty's formulae may be used.

Q3: What coordinate format should I use?
A: Use decimal degrees (e.g., 40.7128° instead of 40°42'46"). The calculator automatically converts degrees to radians for calculation.

Q4: Can I calculate distances in miles?
A: The result is in kilometers. To convert to miles, multiply by 0.621371 (1 km = 0.621371 miles).

Q5: What are the limitations of this calculation?
A: It assumes a perfect sphere and doesn't account for terrain elevation, road networks, or atmospheric conditions that might affect actual travel distance.