Plane from Three Points Calculator

About this calculator

Given three non-collinear points, the plane's normal vector is found by taking the cross product of two edge vectors formed from the points: n = (P₂ − P₁) × (P₃ − P₁). That normal vector's components become the A, B, C coefficients in the plane equation Ax + By + Cz + D = 0, and D is solved by plugging any one of the three points back into the equation.

3D graphics programmers use this to compute surface normals for lighting and collision calculations, CAD and BIM engineers use it to define reference planes and cutting sections from measured points on a model, and surveyors and geodesists use the same cross-product method to fit a best-fit ground plane through three elevation-surveyed points on a site.