Plane Equation Calculator - 3D Geometry Tools | Toolivaa

Plane Equation Calculator

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Plane Equation Calculator

Calculate plane equations in 3D space from points, normal vectors, or intercepts with step-by-step solutions and 3D visualizations.

ax + by + cz + d = 0

Three Points

From 3 non-collinear points

Point & Normal

Point and normal vector

Intercept Form

Using intercepts

Three Points Method

Point A (x₁, y₁, z₁)

x₁

y₁

z₁

Point B (x₂, y₂, z₂)

x₂

y₂

z₂

Point C (x₃, y₃, z₃)

x₃

y₃

z₃

General Form

Normalized

Intercept Form

Parametric

All coordinates are in 3D space. Points must be non-collinear for three-point method.

XY Plane

Parallel to XY plane

z = 0

Simple Plane

x + y + z = 1

(1,0,0), (0,1,0), (0,0,1)

Normal Vector

Normal: (1,2,3)

x + 2y + 3z = 6

Plane Equation Result

Equation Details:

Step-by-Step Calculation:

Plane Analysis:

3D Visualization:

3D representation of the plane in coordinate space

A plane in 3D space is defined by a linear equation ax + by + cz + d = 0.

What is a Plane Equation?

A plane equation in three-dimensional

Plane Equation Calculator