Math

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

Calculated Output

Distance 1

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

Step-by-Step Breakdown

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

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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.