Distance Calculator Between Two Coordinates

Haversine Formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\varphi_2-\varphi_1}{2}\right) + \cos(\varphi_1) \cos(\varphi_2) \sin²\left(\frac{\lambda_2-\lambda_1}{2}\right)}\right) \]

Latitude 1 (φ₁):

Longitude 1 (λ₁):

Latitude 2 (φ₂):

Longitude 2 (λ₂):

Earth Radius (R):

Distance Between Points:

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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 for navigation and geographical calculations.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2 R \arcsin\left(\sqrt{\sin²\left(\frac{\varphi_2-\varphi_1}{2}\right) + \cos(\varphi_1) \cos(\varphi_2) \sin²\left(\frac{\lambda_2-\lambda_1}{2}\right)}\right) \]

Where:

\( \varphi_1, \lambda_1 \) — Latitude and longitude of point 1 (in radians)
\( \varphi_2, \lambda_2 \) — Latitude and longitude of point 2 (in radians)
\( R \) — Radius of the Earth (default 6371 km)
\( d \) — Distance between the two points

Explanation: The formula accounts for the curvature of the Earth by using trigonometric functions to calculate the shortest path (great-circle distance) between two points.

3. Importance of Distance Calculation

Details: Accurate distance calculation between geographical coordinates is essential for navigation systems, flight planning, geographical information systems (GIS), and many location-based services.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees (e.g., 40.7128° N, 74.0060° W as 40.7128, -74.0060). Positive values for North/East, negative for South/West. Earth radius defaults to 6371 km but can be adjusted.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: It's very accurate for most purposes, assuming a perfect sphere. The Earth is actually an oblate spheroid, so more complex formulas like Vincenty's might be needed for extreme precision.

Q2: What's the maximum distance this can calculate?
A: The formula works for any distance on a sphere, but for antipodal points (exactly opposite sides of Earth), special consideration is needed due to floating-point precision.

Q3: Can I use this for celestial objects?
A: Yes, if you know the radius of the celestial body, you can use this formula to calculate distances on its surface.

Q4: Why not use simple Pythagorean theorem?
A: On a sphere, straight lines are great circles. The Pythagorean theorem only works on flat planes and becomes increasingly inaccurate over long distances on Earth.

Q5: What coordinate systems are supported?
A: This calculator uses decimal degrees. If you have coordinates in degrees/minutes/seconds, convert them to decimal degrees first.