Use this Plane Equation from Three Points Calculator to find the equation of a plane given three points in 3D space.
| Point A | Point B | Point C | Plane Equation |
|---|---|---|---|
| (0,0,0) | (1,0,0) | (0,1,0) | z = 0 |
| (1,2,3) | (4,0,1) | (2,3,5) | 2x - y + z - 4 = 0 |
| (0,1,2) | (1,0,3) | (2,1,1) | 3x - y - 2z + 1 = 0 |
| (1,1,1) | (2,3,4) | (0,2,5) | 5x - 2y - 3z + 1 = 0 |
| (0,0,1) | (1,1,0) | (2,0,2) | x - 2y + z -1 = 0 |
1. Compute vectors AB = B - A and AC = C - A.
2. Find cross product n = AB × AC to get plane normal vector (A, B, C).
3. Substitute a point into A(x - x₁) + B(y - y₁) + C(z - z₁) = 0 to get D.
4. Result gives plane equation manually.
This Plane Equation from Three Points Calculator provides accurate results for plane equations in 3D space. Useful for students, engineers, and anyone learning how to find a plane equation from three points.
• Any three non-collinear points define a unique plane.
• Plane equations are fundamental in 3D geometry.
• Used in computer graphics, CAD, and physics.
• The cross product gives a vector perpendicular to the plane.
• Plane equations are used to detect collisions in 3D simulations.