Travel Distance Calculator Australia

Haversine Formula:

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

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 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 locations on Earth, accounting for the planet's curvature.

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 points
\( r \) — Earth's radius (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 latitude
\( \Delta\lambda \) — Difference in longitude

Explanation: The formula accounts for the spherical shape of Earth, providing accurate distance calculations over long distances.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for travel planning, logistics, navigation systems, and geographical analysis. In Australia's vast landscape, understanding true distances between locations is essential for efficient travel and transport.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in decimal degrees. Valid ranges: latitude -90 to 90, longitude -180 to 180. For Australian locations, latitude is typically negative (southern hemisphere).

5. Frequently Asked Questions (FAQ)

Q1: Why use Haversine instead of simple Euclidean distance?
A: Haversine accounts for Earth's curvature, providing accurate results over long distances, while Euclidean distance assumes a flat surface.

Q2: How accurate is this calculation?
A: The Haversine formula provides accuracy within 0.5% for most practical purposes, assuming a spherical Earth model.

Q3: What are typical coordinates for Australian cities?
A: Sydney: -33.8688, 151.2093; Melbourne: -37.8136, 144.9631; Brisbane: -27.4698, 153.0251; Perth: -31.9505, 115.8605.

Q4: Can I use this for driving distances?
A: This calculates straight-line (great-circle) distance. Driving distances will be longer due to roads, terrain, and detours.

Q5: What's the maximum distance I can calculate?
A: The formula works for any two points on Earth, from a few meters to the maximum Earth circumference (~40,075 km).