Great Circle Calculator

How Great Circle Calculator Works?

The Great Circle Calculator models the two coordinates as points on a sphere. Enter the first and second latitudes and longitudes, along with the sphere radius. Latitudes range from −90° to 90°, longitudes from −180° to 180°, and angular values may be expressed in degrees or radians. The radius can be entered in km, m, mi, nmi, ft, or yd.

Let $\phi ₁$ and $\phi ₂$ be the latitudes, $\lambda ₁$ and $\lambda ₂$ be the longitudes, and let $R$ be the sphere radius. The longitude difference is $\mathrm{\Delta \lambda }={\lambda }_2-{\lambda }_1$.

The central angle, or angular separation, is calculated with the haversine relationship. This method is numerically stable for both short and long distances.

The shortest surface distance follows the great-circle arc:

The initial bearing is the forward direction leaving the first point, while the final bearing is the direction of travel as the route reaches the second point. Both use the two-argument arctangent function so that the correct quadrant is preserved.

The midpoint is found by representing the second point in a local three-dimensional form and averaging it with the first point along the great-circle geometry:

Finally, the chord length is the straight-line distance through the sphere between the two surface points:

Practical Use Cases

Navigators can enter departure and destination coordinates to estimate the shortest route over a spherical Earth and obtain both the initial course and arrival bearing. The midpoint coordinates can help identify a halfway checkpoint or divide a long journey into manageable legs.

Geospatial analysts can use the calculator to compare locations, calculate angular separation, and estimate spherical distances for mapping, geographic information systems, spatial databases, and coverage studies.

Travelers can use the great-circle distance to understand the shortest geographic separation between cities or landmarks. The midpoint result provides a useful approximate halfway location for planning itineraries or selecting meeting areas.

Engineers can use the radius input and chord-length output in spherical geometry, antenna coverage, satellite links, spherical construction models, and simulations where surface paths must be distinguished from straight interior lines.

Students and educators can explore how latitude, longitude, central angles, bearings, midpoints, arc distances, and chords relate to one another. Entering known coordinate pairs makes it possible to verify the haversine formula and compare curved surface distance with three-dimensional chord length.

Accuracy and Limitations

The calculator uses double-precision trigonometric formulas for an ideal sphere, so its numerical results are generally reliable for valid latitude, longitude, and positive-radius inputs, including very short separations when the haversine method is used. Its distance accuracy depends on the selected sphere radius: using a single radius does not model Earth's ellipsoidal shape, local elevation, terrain, or geodetic datums. Bearings describe the shortest great-circle route, not a constant-compass or rhumb-line course. Midpoint and bearing results can also become mathematically indeterminate or highly sensitive when the points coincide or are nearly antipodal, because multiple shortest great-circle paths may exist.

Quick Examples