Plane Equation Calculator

Find the equation of a plane from three points or a point and normal vector.

Input Method

Point P₁

Point P₂

Point P₃

Plane Equation (General Form)

1.0000x + 1.0000y + 1.0000z + -1.0000 = 0

Normal Form

0.5774x + 0.5774y + 0.5774z = 0.5774

Normal Vector

n = (1.0000, 1.0000, 1.0000)

|n| = 1.7321

n̂ = (0.5774, 0.5774, 0.5774)

Distance from Origin

0.5774

Coefficients

a=1.00, b=1.00

c=1.00, d=-1.00

Intercepts

x-intercept

1.0000

y-intercept

1.0000

z-intercept

1.0000

General Form

ax + by + cz + d = 0

n = (a, b, c) is normal to the plane

Point-Normal Form

n · (r - r₀) = 0

r₀ is a point on the plane

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Cross product

Point calculations