Latitude Longitude Angle Calculator

Angle Between Coordinates Formula:

\[ \text{angle} = \arccos(\sin(\text{lat1}) \times \sin(\text{lat2}) + \cos(\text{lat1}) \times \cos(\text{lat2}) \times \cos(\text{dlon})) \]

Calculated Angle:

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1. What is the Latitude Longitude Angle Calculator?

The Latitude Longitude Angle Calculator computes the central angle between two points on a sphere (like Earth) given their latitudes and the difference in their longitudes, all in radians.

2. How Does the Calculator Work?

The calculator uses the spherical angle formula:

\[ \text{angle} = \arccos(\sin(\text{lat1}) \times \sin(\text{lat2}) + \cos(\text{lat1}) \times \cos(\text{lat2}) \times \cos(\text{dlon})) \]

Where:

\( \text{lat1} \) — Latitude of first point in radians
\( \text{lat2} \) — Latitude of second point in radians
\( \text{dlon} \) — Difference in longitudes in radians

Explanation: This formula calculates the central angle between two points on a sphere using trigonometric functions of their coordinates.

3. Importance of Angle Calculation

Details: Calculating angles between geographic coordinates is fundamental for navigation, distance calculations, and various geospatial applications.

4. Using the Calculator

Tips: Enter all angles in radians (convert from degrees if necessary). The calculator will compute the central angle between the two points.

5. Frequently Asked Questions (FAQ)

Q1: Why use radians instead of degrees?
A: The trigonometric functions in most programming languages use radians, making this the natural unit for calculations.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q3: What's the range of possible results?
A: The angle will be between 0 and π radians (0 to 180 degrees).

Q4: Can I use this for Earth distance calculations?
A: Yes, multiply the angle by Earth's radius (mean radius ≈ 6,371 km) to get great-circle distance.

Q5: What if my longitudes wrap around 180°?
A: Use the smallest longitude difference (ensure dlon ≤ π radians).