Gpsarea Calculator
Instantly convert gpsarea with our free converter. See conversion tables, formulas, and step-by-step explanations. Enter your values for instant results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Area = 0.5 * |AB x AC| where AB and AC are 3D Cartesian vectors from point A to B and C
Each GPS coordinate is converted from latitude/longitude to 3D Cartesian coordinates using Earth radius (6,371 km). Two edge vectors are formed from the triangle vertices. The cross product magnitude gives twice the triangle area, so we divide by 2. Results are then converted to various area units.
Worked Examples
Example 1: Calculating a Triangular Plot in Manhattan
Problem:Find the area of a triangular plot defined by coordinates (40.7128, -74.006), (40.758, -73.9855), and (40.7484, -73.9857).
Solution:Convert lat/lon to Cartesian (x, y, z) using Earth radius R = 6,371,000 m.\nCompute vectors A = P2 - P1, B = P3 - P1.\nArea = 0.5 * |A x B| (cross product magnitude).\nConvert to desired units.
Result:The area of the triangle is computed from the cross product of the edge vectors in 3D space.
Example 2: Measuring a Farm Parcel
Problem:A farmer has three GPS waypoints at (35.0, -80.0), (35.005, -80.0), and (35.0, -79.995).
Solution:Convert coordinates to meters using Cartesian projection.\nCalculate cross product of edge vectors.\nArea = 0.5 * magnitude of cross product.\nConvert from sq meters to acres: divide by 4046.86.
Result:The triangular parcel measures approximately 126,900 sq meters or 31.36 acres.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy