Free Equation of a Plane Calculator - Given three 3-dimensional points, this calculates the equation of a plane that contains those points.

This calculator has 3 inputs.

This calculator has 3 inputs.

Ax + By + Cz + D = 0

|A| = y_{1}(z_{2} - z_{3}) + y_{2}(z_{3} - z_{1}) + y_{3}(z_{1} - z_{2})

|B| = z_{1}(x_{2} - x_{3}) + z_{2}(x_{3} - x_{1}) + z_{3}(x_{1} - x_{2})

|C| = x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) + x_{3}(y_{1} - y_{2})

|D| = x_{1}(y_{2}z_{3} - y_{3}z_{2}) + x_{2}(y_{3}z_{1} - y_{1}z_{3}) + x_{3}(y_{1}z_{2} - y_{2}z_{1})

For more math formulas, check out our Formula Dossier

|A| = y

|B| = z

|C| = x

|D| = x

For more math formulas, check out our Formula Dossier

- determinant
- value computed from a square matrix

det(A) or |A| - equation
- a statement declaring two mathematical expressions are equal
- equation of a plane
- formula to graph the points in a plane

Ax + By + Cz + D = 0 - matrix
- a rectangular array of numbers or symbols which are generally arranged in rows and columns
- plane
- a flat, two-dimensional surface that extends indefinitely
- point
- an exact location in the space, and has no length, width, or thickness

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