How To Calculate Aerial Distance

Haversine Formula:

\[ Distance = 2 \times R \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta lat}{2}\right) + \cos(lat_1)\cos(lat_2)\sin^2\left(\frac{\Delta lon}{2}\right)}\right) \]

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

Great-circle 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 the shortest distance between two points on the Earth's surface, accounting for the Earth's curvature.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ Distance = 2 \times R \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta lat}{2}\right) + \cos(lat_1)\cos(lat_2)\sin^2\left(\frac{\Delta lon}{2}\right)}\right) \]

Where:

\( R \) — Earth's radius (6371 km)
\( lat_1, lat_2 \) — Latitude of points 1 and 2 in radians
\( lon_1, lon_2 \) — Longitude of points 1 and 2 in radians
\( \Delta lat \) — Difference in latitude
\( \Delta lon \) — Difference in longitude

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

3. Importance of Great-circle Distance

Details: Great-circle distance represents the shortest path between two points on a sphere. This is crucial for aviation, navigation, and geographic information systems where accurate distance calculations are essential.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Latitude ranges from -90° (South Pole) to 90° (North Pole). Longitude ranges from -180° to 180°. Ensure coordinates are within valid ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between great-circle distance and rhumb line?
A: Great-circle distance is the shortest path between two points on a sphere, while a rhumb line maintains a constant bearing and is longer but easier to navigate.

Q2: How accurate is the Haversine formula?
A: The Haversine formula is very accurate for most practical purposes, with errors typically less than 0.5% due to the Earth being an oblate spheroid rather than a perfect sphere.

Q3: Can I use this for very short distances?
A: Yes, but for very short distances (less than 1 km), the flat Earth approximation may be sufficient and simpler to calculate.

Q4: What Earth radius should I use?
A: For most applications, 6371 km (mean radius) is sufficient. For higher precision, you might use 6378.137 km (equatorial radius) or 6356.752 km (polar radius).

Q5: How do I convert degrees to radians?
A: Multiply degrees by π/180. Most programming languages have built-in functions like deg2rad() for this conversion.