Walking Distance Route Calculator

Haversine Formula:

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

Latitude Point 1:

degrees

Longitude Point 1:

degrees

Latitude Point 2:

degrees

Longitude Point 2:

degrees

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 geographic coordinates on Earth.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

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

Where:

\( r \) — Earth's radius (6371 km)
\( \phi_1, \phi_2 \) — Latitude of point 1 and point 2 in radians
\( \lambda_1, \lambda_2 \) — Longitude of point 1 and point 2 in radians
\( \Delta\phi \) — Difference between latitudes
\( \Delta\lambda \) — Difference between longitudes

Explanation: The formula accounts for the spherical shape of the Earth, providing accurate distance calculations between any two points on the globe.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for route planning, navigation systems, logistics, travel planning, and geographic information systems.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees format. Valid ranges are -90 to 90 for latitude and -180 to 180 for longitude.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the Haversine formula?
A: The Haversine formula provides very accurate results for most practical purposes, with errors typically less than 0.5% for Earth's surface.

Q2: Does this calculate walking distance or straight-line distance?
A: This calculates the great-circle (straight-line) distance. Actual walking distance may be longer due to terrain and available paths.

Q3: Can I use this for long distances?
A: Yes, the Haversine formula works accurately for both short and long distances across the globe.

Q4: What coordinate format should I use?
A: Use decimal degrees format (e.g., 40.7128, -74.0060 for New York City).

Q5: Are there alternatives to the Haversine formula?
A: Yes, the Vincenty formula provides even greater accuracy but is more computationally intensive.