Plane from 3 Points

Plane equation and normal vector from three points

Point P₁
Point P₂
Point P₃
x + y + z = 1
Plane equation
x + y + z = 1
Normal vector (a, b, c)
(1, 1, 1)
Normal magnitude |n|
1,732051
Unit normal vector
(0,57735, 0,57735, 0,57735)
Plane from 3 Points3D sketch of three points P₁, P₂, P₃ and the normal vector to the plane they span.nP₁P₂P₃

Über diesen Rechner

The Plane from 3 Points Calculator finds the equation of the plane ax + by + cz = d passing through any three points in 3D space, along with the plane's normal vector and unit normal. It detects collinear points that don't define a plane. Use it for analytic geometry, computer graphics, vectors, and engineering.

Häufige Beispiele

  • P₁(0,0,0), P₂(1,0,0), P₃(0,1,0) → z = 0 (the xy-plane), normal (0, 0, 1)
  • P₁(1,0,0), P₂(0,1,0), P₃(0,0,1) → x + y + z = 1, normal (1, 1, 1)
  • P₁(0,0,2), P₂(2,0,2), P₃(0,2,2) → z = 2, normal (0, 0, 1)
  • P₁(0,0,0), P₂(1,1,1), P₃(2,2,2) → collinear points, no unique plane