Euclidean Distance

Euclidean distance is the most fundamental distance measure in spatial analysis, representing the shortest straight-line path between two points in two-dimensional space. It is calculated as the square root of the sum of squared differences in x and y coordinates. In raster GISGISGeographic Information Systems (GIS) enable users to analyze and visualize spatial data to uncover patterns, relation..., the Euclidean distance tool produces an output surface where each cell value represents the distance from that cell's center to the nearest source feature (point, line, or polygon).

Euclidean distance rasters are generated by computing the straight-line distance from every cell in the study area to the closest source location. The resulting surface provides a continuous gradient of proximity that can be used directly or reclassified for further analysis. Additional outputs may include a direction raster (bearing to nearest source) and an allocation raster (identity of nearest source), enabling assignment of locations to their closest facility or feature.

Environmental scientists use Euclidean distance rasters to measure proximity to water bodies, roads, or pollution sources as inputs to habitat suitability models. Urban planners calculate distance to public services, transit stops, and green spaces for equity analysis. Suitability analysisSuitability AnalysisSuitability analysis evaluates geographic locations against multiple criteria to determine how well each area meets t... frequently uses Euclidean distance layers as criteria factors. Buffer analysisBuffer AnalysisBuffer analysis creates zones of specified distances around geographic features such as points, lines, or polygons. I... uses distance thresholds applied to Euclidean distance surfaces. Retail analysts measure straight-line distance to competitor locations as a competitive intelligenceCompetitive IntelligenceCompetitive intelligence in location analytics involves systematically gathering and analyzing data about competitor ... metric.

Euclidean distance assumes a flat, uniform surface with no barriers to movement, which rarely reflects real-world geography. It does not account for roads, terrain, or land cover that affect actual travel. For more realistic distance modeling, cost distance analysisCost Distance AnalysisCost distance analysis calculates the least accumulative cost of traveling from every cell in a raster to one or more... or network distance measures are preferred. On large geographic scales, the curvature of the Earth means that Euclidean distance increasingly diverges from true geodesic distance, requiring the Haversine formulaHaversine FormulaThe Haversine formula calculates the great-circle distance between two points on a sphere given their latitude and lo... or Vincenty's formulae.