Ponto Médio entre Coordenadas

Midpoint between two geographic coordinates

The midpoint between (φ₁, λ₁) and (φ₂, λ₂) is the point lying on the geodesic (great-circle arc) halfway between them. For short distances (a few kilometers), a simple arithmetic mean works: φ_m = (φ₁+φ₂)/2, λ_m = (λ₁+λ₂)/2. For longer distances, the spherical formula uses 3D unit vectors: convert each point to (x, y, z), average, normalize, and convert back. Example: midpoint between São Paulo (-23.5505, -46.6333) and Rio (-22.9068, -43.1729) lands near Resende/RJ, ~halfway along the Dutra highway. The arithmetic shortcut diverges from the spherical answer as the two points get farther apart or near the poles.

Applications

"Meet in the middle" apps that pick a restaurant or café halfway between two friends; route planning splits a long leg into two; mapping centroids of two markers; logistics that pre-position vehicles between depots; emergency response staging.

FAQ

Is the arithmetic mean always good enough? Below ~200 km and away from polar regions, the error is negligible. For intercontinental midpoints, use the spherical formula — averaging coordinates near the date line gives nonsense results.

Does the midpoint equal half the Haversine distance? Yes — by construction, the geodesic midpoint is equidistant from both endpoints.

Same as "centroid" of two points? Conceptually yes for two points; for three or more, centroid (average of all) differs from a true geographic center.