Point to Plane Distance Calculator
Find the perpendicular distance from (x, y, z) to ax + by + cz + d = 0.
Formula
D = |ax + by + cz + d| / √(a² + b² + c²)
Distance (coordinate unit) ≈ abs((0)×(0)+(0)×(0)+(1)×(5)+(-2))÷sqrt((0)^2+(0)^2+(1)^2)
How to use
- Enter the point coordinates.
- Enter a, b, c and d after moving every term to the left.
- Read the distance in the coordinate unit.
Examples
- (0, 0, 5) to z = 2: D = 3.
Frequently asked questions
Can a, b and c all be zero?
No. A plane needs a nonzero normal vector; the calculation rejects this case.
What units should I use?
Use one common length unit and scale for all coordinates.
What if the point lies on the plane?
The distance is zero; the sign of the plane equation does not change distance.
Sources
Updated: