Distance Between 2 Places Calculator

Haversine Formula:

\[ d = 2r \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \]

Location 1 Latitude:

Location 1 Longitude:

Location 2 Latitude:

Location 2 Longitude:

Distance Unit:

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 distances between locations on Earth.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2r \times \arcsin\left(\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \times \cos(\phi_2) \times \sin^2\left(\frac{\Delta\lambda}{2}\right)}\right) \]

Where:

\( d \) — Distance between two points
\( r \) — Earth's radius (3959 miles or 6371 km)
\( \phi_1, \phi_2 \) — Latitudes of point 1 and 2 in radians
\( \lambda_1, \lambda_2 \) — Longitudes of point 1 and 2 in radians
\( \Delta\phi \) — Difference in latitudes
\( \Delta\lambda \) — Difference in longitudes

Explanation: The formula accounts for the spherical shape of the Earth, providing accurate great-circle distances rather than straight-line distances on a flat surface.

3. Importance of Distance Calculation

Details: Accurate distance calculation is essential for navigation, logistics, travel planning, geographic analysis, and various scientific applications involving spatial relationships.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Valid ranges: latitude -90° to 90°, longitude -180° to 180°. Select preferred distance unit (miles or kilometers).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between great-circle distance and straight-line distance?
A: Great-circle distance follows the curvature of the Earth, representing the shortest path between two points on a sphere, while straight-line distance assumes a flat surface.

Q2: How accurate is the Haversine formula?
A: The Haversine formula is very accurate for most practical purposes, typically within 0.5% of the actual great-circle distance.

Q3: Can I use this for very short distances?
A: Yes, but for distances under 1 km/mile, flat-Earth approximations may be sufficient and computationally simpler.

Q4: What coordinate format should I use?
A: Use decimal degrees format (e.g., 40.7128° instead of 40°42'46"). Most GPS devices and mapping services provide coordinates in this format.

Q5: Does this account for elevation differences?
A: No, the Haversine formula calculates horizontal distance only and does not consider elevation differences between locations.