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 distances between cities on Earth.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

Where:

• \( lat1 \) — Latitude of first point in radians
• \( lat2 \) — Latitude of second point in radians
• \( \Delta lon \) — Difference in longitude between the two points in radians
• 3959 — Earth's radius in miles

Explanation: The formula calculates the shortest distance between two points on the surface of a sphere, following the great-circle path.

3. Importance of Great-Circle Distance

Details: Great-circle distance is essential for navigation, flight planning, and geographical analysis as it represents the shortest path between two points on a sphere.

4. Using the Calculator

Tips: Enter all coordinates in radians. Remember to convert degrees to radians by multiplying by π/180. Ensure longitude difference is calculated correctly.

5. Frequently Asked Questions (FAQ)

Q1: Why use radians instead of degrees?
A: Trigonometric functions in mathematical calculations typically require radians for accurate results.

Q2: How accurate is the Haversine formula?
A: It's very accurate for most practical purposes, assuming a spherical Earth with radius 3959 miles.

Q3: What's the difference between great-circle and rhumb line distance?
A: Great-circle is the shortest path, while rhumb line maintains constant bearing and is longer.

Q4: Can I use this for very short distances?
A: Yes, but for very short distances, planar approximation might be sufficient and simpler.

Q5: Why is Earth's radius 3959 miles?
A: This is the mean radius of Earth. The actual radius varies from about 3950 to 3963 miles.