Let a plane \(P\) be given by the equation:
\[ a x + b y + c z + d = 0 \]
and a point \(M\) by its coordinates \((x_0, y_0, z_0)\). The Euclidean distance \(D\) from \(M\) to plane \(P\) is:
\[ D = \frac{ |\,a x_0 + b y_0 + c z_0 + d\,| }{ \sqrt{a^2 + b^2 + c^2} } \]
Distance from point to a plane calculator
shortest distance between a point and a plane (Cartesian coordinates)
Point M (x₀, y₀, z₀)
Plane coefficients (a, b, c, d)
plane equation: a·x + b·y + c·z + d = 0
—units
formula used: D = |a·x₀ + b·y₀ + c·z₀ + d| / √(a² + b² + c²)