Rhumb line midpoint calculator

This calculator finds the coordinate halfway along that constant-bearing path between two supplied latitude and longitude points. It uses spherical rhumb geometry rather than averaging both coordinates, so the result remains meaningful on long routes and paths that cross the antimeridian. Enter decimal-degree coordinates, choose the output precision, and receive a normalized midpoint suitable for navigation calculations, mapping workflows, route labels, or independent verification.

What a rhumb line midpoint represents

The midpoint returned here is the halfway position along a spherical rhumb line, not the midpoint of a great-circle arc and not simply the arithmetic average of two latitude and longitude pairs. A rhumb line maintains one constant compass bearing as it crosses successive meridians. That property made loxodromes especially useful for traditional marine navigation and still makes them relevant when a route is intentionally described by a fixed heading. Latitude changes uniformly along the spherical formulation, while longitude must be evaluated through isometric latitude, a logarithmic transformation used in Mercator geometry. The distinction matters because longitude spacing represents different surface distances at different latitudes. On a short local segment, several midpoint methods may look nearly identical, but the difference becomes visible across large north-south spans or near high latitudes. Use this result when the underlying route is explicitly a constant-bearing path. If your route follows the shortest surface arc instead, a great-circle midpoint calculator describes a different geometric object and should be used instead.

How to enter coordinates and interpret the result

Provide the starting latitude and longitude as lat1 and lon1, then the ending values as lat2 and lon2. Coordinates are decimal degrees: latitude is negative south of the equator and positive north of it, while longitude is negative west of Greenwich and positive east. Longitudes may include either endpoint of the conventional −180 to 180 degree range. Exact north and south pole latitudes are rejected because the isometric-latitude expression becomes singular there; values close to a pole remain valid. The response contains lat and lon for the point halfway along the loxodrome. Longitude is normalized to the standard range, which is important when the shortest constant-bearing route crosses the antimeridian. For example, a path from 170 degrees east to 170 degrees west should pass near 180 degrees, not sweep through Greenwich. The optional precision field controls decimal places from zero through twelve. It changes presentation and rounding only; it does not switch the geometric model or imply real-world survey accuracy.

Method, assumptions, and practical limits

The calculation treats the Earth as a sphere and applies the standard loxodromic midpoint relationship. It first converts both latitudes to radians, takes their halfway latitude, and then determines the matching longitude by comparing logarithms of Mercator projection factors. When both endpoints have effectively the same latitude, the logarithmic denominator approaches zero, so the algorithm uses the midpoint of the unwrapped longitudes instead. Before that calculation, an antimeridian crossing is unwrapped onto the shorter longitudinal interval; the final longitude is then normalized again. This approach is deterministic and uses no network service, stored route data, random values, or current time. A spherical answer is appropriate for navigation estimates, map annotation, educational work, and consistency checks. It is not a cadastral or geodetic survey solution, because the Earth is better represented by an ellipsoid for high-precision physical positioning. Also remember that a rhumb path is generally longer than a great-circle route, except along special tracks such as the equator or a meridian. The API price is $0.002 per request.