Calculate Nautical Miles Between Locations

Haversine Formula:

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

Latitude 1:

Longitude 1:

Latitude 2:

Longitude 2:

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 as it provides accurate distance measurements on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

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

Where:

\( d \) — Distance in nautical miles
\( R \) — Earth's radius (3440 nautical miles)
\( \phi_1, \phi_2 \) — 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 flat-Earth approximations, especially for longer distances.

3. Importance of Accurate Distance Calculation

Details: Accurate distance measurement is crucial for navigation, flight planning, maritime operations, and any application requiring precise location-based calculations.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees (e.g., 34.0522° N should be entered as 34.0522). Positive values for North/East, negative for South/West.

5. Frequently Asked Questions (FAQ)

Q1: Why use nautical miles instead of statute miles or kilometers?
A: Nautical miles are based on the Earth's circumference and are the standard unit for maritime and aviation navigation.

Q2: How accurate is this calculation?
A: The formula assumes a perfect sphere. The Earth is actually an oblate spheroid, but the error is typically less than 0.5% for most practical purposes.

Q3: Can I use this for very short distances?
A: Yes, though for distances under 1 nautical mile, flat-Earth approximations may be sufficient.

Q4: What's the maximum distance this can calculate?
A: The formula works for any distance, but for antipodal points (exactly opposite sides of the Earth), special consideration is needed.

Q5: How does altitude affect the calculation?
A: This formula ignores altitude differences and calculates distance as if both points are at sea level.