Great Circle Distance

GEOGRAPHY & CARTOGRAPHY CALCULATOR Great Circle Distance A precise tool.
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What is the Great Circle Distance & How does it work?
A great‑circle is the intersection of a sphere with a plane that passes through the sphere’s centre. On Earth, the shortest path between two locations follows a great‑circle, which appears as a curved line on most map projections. The central angle Δσ between the two points can be obtained from their latitudes (φ₁, Ο†β‚‚) and longitudes (λ₁, Ξ»β‚‚) using the haversine formula. This relationship is expressed mathematically as:
Deltasigma = 2cdotarcsin!Bigl(sqrt{sin^{2}!bigl(frac{Deltaphi}{2}bigr) + cos phi_{1} cos phi_{2} sin^{2}!bigl(frac{Deltalambda}{2}bigr)}Bigr)
Δσ = central angle (radians)
Once Δσ is known, the great‑circle distance d is simply the product of the Earth’s mean radius R and the central angle: d = R·Δσ. This calculation underpins navigation, aviation, and many GIS analyses.
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Frequently Asked Questions
What is a great-circle distance?
A great-circle distance is the shortest path between two points on the surface of a sphere, like the Earth.
How do I use the haversine formula to calculate this distance?
Input the latitudes and longitudes of the two points into the formula to find the central angle, then multiply by the radius of the Earth for the distance.
Why is a great-circle path the shortest?
A great-circle path follows the curvature of the Earth, making it the shortest route between two points on its surface.
Can this calculator be used for any spherical object?
Yes, but you would need to adjust the radius of the sphere in the formula to match the object’s size.
What is the difference between a great-circle and a rhumb line?
A great-circle path is the shortest distance on a sphere, while a rhumb line follows a constant bearing and appears as a straight line on some map projections.
How accurate is this calculator for small distances?
For very short distances, other factors like terrain and local geography can affect accuracy more than the method used to calculate the distance.
Is there a limit to how far apart the two points can be?
No, this formula works for any two points on a sphere, regardless of their distance apart.

Results are for informational purposes only and do not constitute professional advice.