Distance By Sea Calculator

Haversine Formula:

\[ Distance = 2 \times R \times \arcsin\left(\sqrt{\sin^2\left(\frac{lat2 - lat1}{2}\right) + \cos(lat1) \times \cos(lat2) \times \sin^2\left(\frac{lon2 - lon1}{2}\right)}\right) \]

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

Distance (Nautical Miles):

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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 nautical distances over the Earth's surface, accounting for the spherical shape of our planet.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 2 \times R \times \arcsin\left(\sqrt{\sin^2\left(\frac{lat2 - lat1}{2}\right) + \cos(lat1) \times \cos(lat2) \times \sin^2\left(\frac{lon2 - lon1}{2}\right)}\right) \]

Where:

\( R \) — Earth's radius (3440 nautical miles)
\( lat1, lon1 \) — Latitude and longitude of first point (degrees)
\( lat2, lon2 \) — Latitude and longitude of second point (degrees)
All trigonometric functions use radians

Explanation: The formula calculates the central angle between two points and multiplies by the Earth's radius to get the great-circle distance.

3. Importance of Nautical Distance Calculation

Details: Accurate nautical distance calculation is crucial for maritime navigation, voyage planning, fuel estimation, and safety at sea. It helps determine the shortest route between two points on the ocean.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Latitude ranges from -90° to 90° (negative for southern hemisphere), longitude ranges from -180° to 180° (negative for western hemisphere).

5. Frequently Asked Questions (FAQ)

Q1: Why use nautical miles instead of regular miles?
A: Nautical miles are based on the Earth's circumference and are the standard unit for maritime and aviation navigation (1 nautical mile = 1 minute of latitude).

Q2: How accurate is the haversine formula?
A: The haversine formula provides excellent accuracy for most practical navigation purposes, typically within 0.5% of the actual great-circle distance.

Q3: What's the difference between great-circle and rhumb line distance?
A: Great-circle distance is the shortest path between two points on a sphere, while rhumb line maintains a constant compass bearing. Great-circle is shorter but requires constant course adjustments.

Q4: Can I use this for air distance calculations?
A: Yes, the haversine formula works equally well for air navigation, though aviation typically uses nautical miles as well.

Q5: What about elevation differences?
A: The haversine formula calculates surface distance only. For precise calculations involving significant elevation differences, additional corrections would be needed.