Enter the equation of a plane and the coordinates of a point to calculate the distance from the point to the plane.

Distance from point to plane formula

The following equation can be used to calculate the distance between a plane and a point.

d = |A·X + B·Y + C·Z + D/ √A2 + B2 + C2

  • Where D is the distance
  • A, B, C, and D are constants of the plane equation
  • X, Y, and Z are the coordinate points of the point

Distance From Point to Plane Definition

The distance from a point to a plane is defined as the shortest distance from a single point to any point on a plane.

How to calculate the distance from a point to a plane?

How to calculate the distance from a point to a plane

  1. First, determine the equation of the plane.

    A 3-dimensional plane can be represented using an equation in the form AX + BY + CZ + D.

  2. Next, gather the constants from the equation in stead 1.

    Separate A, B, and C in the equation determined in step 1.

  3. Next, determine the coordinates of the point

    Measure or calculate the coordinates of the points x,y, and z.

  4. Calculate the distance

    Calculate the distance from the point to the plane using the equation above and information from steps 1-3.

FAQ

How can you calculate a distance from a point to a plane when the plane is everywhere?

Great question. The answer to this is that you can only calculate the average distance to the plane which will be a point directly perpendicular to the point and plane.