Plane Through a Point with a Normal Vector (3D) Calculator

Published on: May 10, 2026
Final Answer: Free • Full Steps: Pro

This Plane Through a Point with a Normal Vector (3D) Calculator helps you find the equation of a plane in three-dimensional space from a given point and normal vector. Use the point as a known position on the plane and the normal vector to determine the plane’s orientation. Then substitute those values 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 point P₀ = (x₀,y₀,z₀) and normal vector n = ⟨a,b,c⟩.
  2. Use the point-normal plane equation.
  3. Substitute the point and normal vector, then simplify to standard form.

Formula:

\(a\left(x - x_{0}\right) + b\left(y - y_{0}\right) + c\left(z - z_{0}\right) = 0\)