Work out point to plane distance instantly with clear inputs, formula shown and shareable results.
For the plane ax + by + cz + d = 0 the perpendicular distance from a point is |ax₀ + by₀ + cz₀ + d| / √(a² + b² + c²). Keeping the sign tells you which side of the plane the point lies on.
Point-plane distance
D = |ax₀ + by₀ + cz₀ + d| / √(a² + b² + c²)
The numerator is |2 − 6 + 18 − 5| = 9 and |n| = 7, so the distance is 9/7 ≈ 1.285714.
The sign follows the direction of the normal vector (a, b, c); reversing all four coefficients flips the sign but not the distance.