Plane Through Three Points (3D) Calculator

Published on: May 17, 2026
Final Answer: Free • Full Steps: Pro

This Plane Through Three Points (3D) Calculator helps you find the equation of a plane in three-dimensional space that passes through three given points. First form two direction vectors from the points, then use their cross product to find a normal vector to the plane. Substitute that normal vector and one of the points into the point-normal form and simplify to get the equation. It is a simple way to check answers, understand the method clearly, and practise 3D coordinate geometry step by step.

Step-by-step method

  1. Identify the three points P₁, P₂, P₃.
  2. Find two direction vectors in the plane and compute the normal vector n = v × w.
  3. Use the point-normal plane equation and simplify.

Formula:

\(\vec{n} = \left(P_{2} - P_{1}\right) \times \left(P_{3} - P_{1}\right)\)