Trace spherical routes with precise geodesic distance outputs. Compare bearings, midpoints, and sampled segments easily. Create navigation-ready results for research, fieldwork, and teaching today.
| Case | Start (lat, lon) | End (lat, lon) | Notes |
|---|---|---|---|
| Karachi → London | 24.8607, 67.0011 | 51.5074, -0.1278 | Intercontinental route and bearing demonstration. |
| Quito → Nairobi | -0.1807, -78.4678 | -1.2921, 36.8219 | Near-equatorial case for spherical interpolation. |
| Sydney → Auckland | -33.8688, 151.2093 | -36.8485, 174.7633 | Shorter arc with clear midpoint shift. |
For two points on a sphere, convert degrees to radians and compute the haversine term:
The central angle and distance are:
Initial bearing from the start point is:
A great-circle path is the shortest route on a sphere. On long ranges, straight lines on map projections can mislead. In physics, this arc length connects angular separation to travel time when speed is approximately constant. This calculator reports arc length and angular separation used by many navigation and geophysics workflows.
Latitude is limited to −90° to 90°, and longitude to −180° to 180°. These bounds match common GPS and GIS exports. Normalized inputs reduce date-line ambiguity and keep bearings interpretable as clockwise angles from true north.
The tool supports a mean Earth radius of 6,371,008.8 m, an equatorial radius of 6,378,137.0 m, and a polar radius of 6,356,752.314245 m. The equatorial–polar difference is about 21.4 km, so long-arc distance can shift by roughly 0.3%. Use a custom radius to model other planets or laboratory spheres.
Distance is computed with the haversine relation, which remains stable for short and long separations. The central angle Δσ is returned in radians and degrees, and the distance is R·Δσ. When Δσ approaches π, points are nearly antipodal and several routes can be similar.
The initial bearing indicates the heading at departure, while the final bearing is the heading upon arrival. On a sphere, bearing generally changes along the route. For aviation and marine use, bearings are shown in a 0–360° convention for direct comparison with compass headings.
The midpoint is computed on the sphere, not by averaging latitudes and longitudes. For plotting or waypoint generation, the calculator can sample up to 200 intermediate points using spherical linear interpolation. A fraction of 0.25 means the point lies one quarter of the angular arc from the start.
Distances may be displayed in meters, kilometers, miles, or nautical miles (1 nmi = 1,852 m). Precision controls formatting on screen without changing internal computation. CSV export includes all metrics and sampled points for direct import into spreadsheets, scripts, and mapping tools.
This calculator assumes a spherical model, appropriate for teaching, visualization, and first-pass engineering. For sub-kilometer surveying or high-accuracy geodesy, an ellipsoidal model (such as WGS84) can be required. Compare outputs across the radius presets to estimate sensitivity for your route.
1) What is the difference between great-circle distance and map distance?
Great-circle distance follows the shortest arc on a sphere. Map distance often measures straight lines on a projection, which can overestimate long routes, especially near the poles.
2) Which Earth radius should I choose for typical global travel?
The mean radius is a solid default for general navigation and education. If you want a quick sensitivity check, compare mean vs equatorial vs polar to see the spread.
3) Why do my bearings change along the route?
A great-circle is not a constant-compass heading except on meridians and the equator. The initial and final bearings differ because the tangent direction evolves along the curved path.
4) What does the central angle represent physically?
The central angle is the angle between the two radius vectors from the sphere’s center. Multiply that angle (in radians) by the radius to obtain the arc length.
5) How should I interpret the intermediate points table?
Each row is a waypoint on the great-circle path, including the start and end. The fraction is the normalized progress along the arc from 0 to 1.
6) Can I use this for other planets or custom spheres?
Yes. Select the custom radius option and enter the sphere radius in meters. The same spherical geometry applies to any idealized planet or laboratory model.
7) Why might results differ from online flight-distance tools?
Some tools use ellipsoidal geodesics and Earth reference frames, while this calculator uses a sphere. Small differences are expected; use the radius presets to bracket outcomes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.