How this calculator works
A plane consists of all points whose displacement from a known point is perpendicular to a normal vector. For three points, crossing two displacement vectors supplies a normal. Collinear or repeated points do not determine a unique plane. Multiplying every coefficient by the same nonzero constant describes the same plane. Axis intercepts are omitted when the corresponding coefficient is zero.
Formula
N = (Q-P) cross (R-P); D = -N dot P; Ax + By + Cz + D = 0.
Worked example
Points (0, 0, 1), (1, 0, 1) and (0, 1, 1) give normal (0, 0, 1), so the plane is z - 1 = 0. Its z intercept is 1.
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Frequently asked questions
Does point order matter?
Reversing two points may reverse every coefficient. The geometric plane stays the same.
Can the normal be a unit vector?
Yes, but it need not be. The calculator also returns its normalised direction.
Why is an intercept missing?
If its coefficient is zero, that axis either never meets the plane or lies entirely in it, so no unique intercept exists.