Equation of a Plane Calculator
Find D in Ax+By+Cz+D=0 from a normal vector and a point.
Formula
Ax+By+Cz+D=0; D=−(Ax₀+By₀+Cz₀).
Constant D ≈ -((2)×(1)+(3)×(3)+(-1)×(-1))
How to use
- Enter normal components A,B,C.
- Enter one point x₀,y₀,z₀.
- Insert D into the plane equation.
Examples
- Normal (2,3,−1) through (1,3,−1) gives 2x+3y−z−12=0.
Frequently asked questions
Can the normal be zero?
No. At least one of A,B,C must be nonzero.
Can I start with three points?
First take the cross product of two difference vectors to find the normal, then use one point here.
Is the equation unique?
Multiplying all four coefficients by the same nonzero number describes the same plane.
Sources
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