basic

Plane Equation from 3 Points Calculator

Compute a, b, c, d in ax + by + cz = d from three 3-D points.

Compute the equation of the plane passing through three 3-D points P, Q, R. The normal vector is the cross product (Q − P) × (R − P), and d = n · P.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

n = (Q − P) × (R − P); ax + by + cz = n · P.

In depth

Compute the equation of the plane passing through three 3-D points P, Q, R. The normal vector is the cross product (Q − P) × (R − P), and d = n · P.