Distance And Mileage Calculator

Haversine Distance Formula:

\[ Distance = \sqrt{ (\Delta lat)^2 + (\Delta long \times \cos(lat))^2 } \times 111 \]

Distance (miles):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Haversine Distance Formula?

The Haversine formula is a mathematical equation used to calculate the great-circle distance between two points on a sphere given their longitudes and latitudes. This approximation provides accurate distance calculations for geographical coordinates on Earth.

2. How Does The Calculator Work?

The calculator uses the Haversine approximation formula:

\[ Distance = \sqrt{ (\Delta lat)^2 + (\Delta long \times \cos(lat))^2 } \times 111 \]

Where:

\( \Delta lat \) — Difference in latitude between two points (degrees)
\( \Delta long \) — Difference in longitude between two points (degrees)
\( lat \) — Reference latitude for cosine correction (degrees)
111 — Conversion factor from degrees to miles

Explanation: The formula accounts for the Earth's curvature by applying a cosine correction to longitude differences based on latitude, providing more accurate distance measurements than simple Euclidean distance.

3. Importance Of Distance Calculation

Details: Accurate distance calculation is essential for navigation, logistics planning, geographic analysis, and various applications in transportation, mapping, and location-based services.

4. Using The Calculator

Tips: Enter latitude difference (Δlat) and longitude difference (Δlong) in degrees, along with the reference latitude. The calculator will provide the distance in miles between the two geographical points.

5. Frequently Asked Questions (FAQ)

Q1: Why Use Haversine Instead Of Simple Distance Formulas?
A: Haversine accounts for the Earth's spherical shape, providing more accurate results for geographical distances compared to flat-Earth approximations.

Q2: How Accurate Is This Approximation?
A: This approximation is highly accurate for most practical purposes, especially for distances up to a few hundred miles. For very long distances, more complex spherical trigonometry may be needed.

Q3: What Units Should I Use For Input Values?
A: All angular measurements should be in degrees. The output distance is calculated in miles.

Q4: Why Is The Cosine Correction Applied To Longitude?
A: Longitude lines converge at the poles, so the actual distance represented by a degree of longitude decreases as you move away from the equator. The cosine correction accounts for this effect.

Q5: Can I Use This For Navigation Purposes?
A: While accurate for general distance calculations, for precise navigation applications, consider using more sophisticated GPS-based calculations that account for altitude and other factors.