Calculate Km Between Two Points

Haversine Formula:

\[ d = 6371 \times \arccos(\sin(lat1)\sin(lat2) + \cos(lat1)\cos(lat2)\cos(lon2-lon1)) \]

Point 1 Latitude:

degrees

Point 1 Longitude:

degrees

Point 2 Latitude:

degrees

Point 2 Longitude:

degrees

Distance Between Points:

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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 accurate for calculating distances between points on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 6371 \times \arccos(\sin(lat1)\sin(lat2) + \cos(lat1)\cos(lat2)\cos(lon2-lon1)) \]

Where:

\( lat1, lon1 \) — Latitude and longitude of point 1 (in degrees)
\( lat2, lon2 \) — Latitude and longitude of point 2 (in degrees)
6371 — Mean radius of the Earth in kilometers

Explanation: The formula accounts for the curvature of the Earth by using trigonometric functions to calculate the shortest distance (great-circle distance) between two points.

3. Importance of Distance Calculation

Details: Accurate distance calculation between geographic points is crucial for navigation, logistics, geography studies, and many location-based applications.

4. Using the Calculator

Tips: Enter latitude and longitude for both points in decimal degrees format. Positive values for North/East, negative for South/West. Example: 40.7128° N, 74.0060° W would be entered as 40.7128, -74.0060.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculation?
A: The Haversine formula is accurate to about 0.3% for most practical purposes on Earth, assuming a spherical Earth model.

Q2: What's the difference between this and Vincenty's formula?
A: Vincenty's formula accounts for Earth's ellipsoidal shape and is more accurate (to within 0.5mm), but more computationally intensive.

Q3: Can I use this for very short distances?
A: Yes, though for distances under 1km, Euclidean distance with projected coordinates might be simpler and equally accurate.

Q4: What coordinate system should I use?
A: Use decimal degrees in WGS84 coordinate system (used by GPS). Convert from DMS if necessary (e.g., 40°42'46"N → 40.7128).

Q5: Why does the Earth's radius affect the calculation?
A: The formula calculates the central angle between points, which must be multiplied by the sphere's radius to get actual distance.