Distance Point To Plane Calculator

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Distance from Point to Plane

Calculate the shortest distance between a point and a plane in 3D space.

Last updated: June 2026 | By Patchworkr Team

Point to Plane Solver
Point P(x0, y0, z0)
Plane Ax + By + Cz + D = 0
Distance
5
Distance is always nonnegative.
d = |1(1) + 2(2) + 2(3) + 4)| / √(1² + 2² + 2²) = 15 / 3 = 5

Point to Plane Distance

The shortest distance from a point to a plane is measured along the line perpendicular to the plane.

How to Use the Formula

  1. Plug the point coordinates into Ax0 + By0 + Cz0 + D.
  2. Take the absolute value of the numerator.
  3. Divide by the length of the normal vector sqrt(A^2 + B^2 + C^2).

Worked Example

P(1, 2, 3) and x + 2y + 2z + 4 = 0 gives distance 5.

The numerator is 15 and the denominator is 3, so the result is 5.

Frequently Asked Questions

What if the point lies on the plane?

Then the numerator is zero and the distance is zero.

Can the plane coefficients all be zero?

No. At least one of A, B, or C must be nonzero to define a plane.

Does this accept decimals?

Yes. The calculator accepts decimals and scientific notation as long as the values are finite.

Why is there an absolute value in the formula?

Distance is a magnitude, so it must be nonnegative even if the signed expression is negative.

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