Distance Between Two Locations Calculator

Great Circle Distance Formula:

\[ d = R \times \arccos[\sin(\phi_1) \times \sin(\phi_2) + \cos(\phi_1) \times \cos(\phi_2) \times \cos(\Delta\lambda)] \]

Latitude of Point 1:

degrees

Longitude of Point 1:

degrees

Latitude of Point 2:

degrees

Longitude of Point 2:

degrees

Great Circle Distance:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Great Circle Distance?

The great-circle distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere. For Earth, this represents the shortest path between two locations (as the crow flies).

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 the two points
\( R \) — Earth's radius (6371 km)
\( \phi_1, \phi_2 \) — Latitude of point 1 and point 2 (in radians)
\( \Delta\phi \) — Difference between latitudes (in radians)
\( \Delta\lambda \) — Difference between longitudes (in radians)

Explanation: The formula calculates the central angle between two points and converts it to distance using Earth's radius.

3. Importance of Distance Calculation

Details: Great circle distance is essential for navigation, flight planning, telecommunications, and any application requiring accurate distance measurements between global locations.

4. Using the Calculator

Tips: Enter latitude (-90 to 90) and longitude (-180 to 180) in decimal degrees for both locations. Positive values are North/East, negative values are South/West.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculation?
A: The calculation assumes a perfect sphere. Earth is an oblate spheroid, so actual distances may vary by up to 0.3%.

Q2: What's the difference between great circle and rhumb line?
A: Great circle is the shortest path, while rhumb line maintains constant bearing (longer but easier to navigate).

Q3: Can I use this for very short distances?
A: For distances under 20 km, planar approximation may be sufficient, but this calculator will still work.

Q4: Why does the formula use radians?
A: Trigonometric functions in most programming languages use radians, so conversion from degrees is necessary.

Q5: How does altitude affect the calculation?
A: This calculation ignores altitude differences, as they're negligible compared to Earth's radius.