Distance from Point to Plane Calculator

Find the distance from a point to the plane ax + by + cz + d = 0.

Point x

Point y

Point z

Distance 1

Formula: distance = |a·x₀ + b·y₀ + c·z₀ + d| ÷ √(a² + b² + c²)

Step-by-step with your numbers:

1. Values used:

2. a = 2

3. b = -1

4. c = 2

5. d = -3

6. Point x = 1

7. Point y = 2

8. Point z = 3

10. Distance = a + b = 2 + -1 = 1

Did we solve your problem today?

Find the perpendicular distance between a point and a plane in 3D space.

The math behind it

Plug the point into the plane expression, take the absolute value, and divide by the magnitude of the normal vector (a, b, c).

Point (1, 2, 3) to 2x − y + 2z − 3 = 0 → |2 − 2 + 6 − 3| ÷ 3 = 1.

What if the point lies on the plane?

The distance is 0 — the numerator becomes zero.