Haversine Formula To Calculate Distance

Haversine Formula:

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

Latitude 1 (radians):

radians

Longitude 1 (radians):

radians

Latitude 2 (radians):

radians

Longitude 2 (radians):

radians

Earth Radius:

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 in navigation and geography for calculating the shortest distance between two points on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

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

Where:

\( lat1, lat2 \) — Latitude coordinates in radians
\( lon1, lon2 \) — Longitude coordinates in radians
\( R \) — Earth's radius (6371 km or 3959 miles)

Explanation: The formula accounts for the spherical shape of the Earth, providing the shortest distance (great-circle distance) between two points.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for navigation systems, flight planning, maritime navigation, and geographic information systems (GIS). It's also used in various applications like location-based services and mapping software.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in radians. The default Earth radius is set to 6371 km (mean Earth radius). For miles, use 3959. All values must be valid numerical inputs.

5. Frequently Asked Questions (FAQ)

Q1: Why use radians instead of degrees?
A: Trigonometric functions in programming languages typically use radians. If you have degrees, convert them to radians first (radians = degrees × π/180).

Q2: How accurate is the Haversine formula?
A: The formula is very accurate for most practical purposes, though it assumes a perfect sphere. The Earth is actually an oblate spheroid, but the difference is negligible for most applications.

Q3: What's 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 compass bearing.

Q4: Can I use this for very short distances?
A: Yes, but for very short distances (less than 1 km), simpler formulas like the Pythagorean theorem might be sufficiently accurate and easier to compute.

Q5: What's the maximum distance this formula can calculate?
A: The formula works for any distance on Earth, up to the maximum possible distance between two points (approximately 20,000 km).