Haversine Formula Distance Calculator

Haversine Formula:

\[ d = 2 \times R \times \arcsin\left(\sqrt{\sin²\left(\frac{\phi_2 - \phi_1}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin²\left(\frac{\lambda_2 - \lambda_1}{2}\right)}\right) \]

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 important for navigation and geographical applications where precise distance measurements are needed.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2 \times R \times \arcsin\left(\sqrt{\sin²\left(\frac{\phi_2 - \phi_1}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin²\left(\frac{\lambda_2 - \lambda_1}{2}\right)}\right) \]

Where:

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

Explanation: The formula accounts for the curvature of the Earth, providing more accurate results than simple Euclidean distance calculations for geographical points.

3. Importance of Great-Circle Distance

Details: Great-circle distance represents the shortest path between two points on a sphere, making it essential for air and sea navigation, GPS systems, and geographical analysis.

4. Using the Calculator

Tips: Enter latitude and longitude in decimal degrees (e.g., 40.7128° N, 74.0060° W as 40.7128, -74.0060). 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 practical purposes, with errors typically less than 0.3% when calculating distances on Earth.

Q2: What's the difference between Haversine and Vincenty formulas?
A: Vincenty's formulae are more accurate (accounting for Earth's ellipsoidal shape) but more computationally intensive.

Q3: What is the maximum distance this can calculate?
A: The formula works for any distance, but for antipodal points (exactly opposite sides of Earth), special consideration is needed.

Q4: Can I use this for other planets?
A: Yes, but you'll need to substitute the appropriate planetary radius for R.

Q5: Why is the Earth's radius 6371 km?
A: This is the mean radius of Earth, which provides a good balance for global distance calculations.