Mileage Distance Calculator United States

Haversine Distance 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 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

Distance (miles):

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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, accounting for the planet's curvature.

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 (3958.8 miles)
\( \phi_1, \phi_2 \) — Latitude of point 1 and 2 in radians
\( \lambda_1, \lambda_2 \) — Longitude of point 1 and 2 in radians
\( \Delta\phi \) — Difference in latitude
\( \Delta\lambda \) — Difference in longitude

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

3. Importance of Distance Calculation

Details: Accurate distance calculation is essential for travel planning, logistics, navigation systems, and geographical analysis. The Haversine formula provides precise straight-line distances accounting for Earth's spherical shape.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Valid ranges: latitude -90 to 90, longitude -180 to 180. Positive values for North/East, negative for South/West.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between straight-line and driving distance?
A: Straight-line distance is the shortest path between two points, while driving distance follows actual roads and can be significantly longer due to terrain and road networks.

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

Q3: Can I use this for international locations?
A: While designed for US locations, the formula works for any coordinates worldwide as long as they're in decimal degrees.

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

Q5: Why does the calculator use Earth radius in miles?
A: This calculator is optimized for US users who typically use miles. For kilometers, multiply the result by 1.60934.