Distances

Distance is a measure of the separation between two points or objects. In everyday life this usually means spatial separation, such as the length from one place to another. In mathematics, distance is formalized as a metric: a function that assigns a nonnegative number to any pair of points, representing how far apart they are.

Common distance measures include Euclidean distance, Manhattan distance, and Chebyshev distance, each arising from a different way of combining coordinate differences. In general, a distance function, or metric, must satisfy non-negativity, identity of indiscernibles, symmetry, and the triangle inequality.

Geographic distances on Earth's surface are usually measured as great-circle distances, the shortest path along the sphere. They are computed from latitude and longitude using formulas such as haversine or Vincenty. Distances are expressed in units such as meters, kilometers, or miles; in astronomy, distances use astronomical units, light-years, or parsecs.

Distances also appear in other domains. In computer science, distance measures quantify difference, such as edit distance between strings or graph distance between nodes. In physics, spacetime intervals combine space and time with the speed of light, so separation can depend on the observer.

Measurement of distance uses methods and instruments appropriate to the scale: rulers and tapes for short ranges; laser rangefinders, radar, or sonar for larger distances; parallax and standard candles for astronomical scales. Accuracy and uncertainty depend on the method and context.