Enter the equation of a plane and the coordinates of a point to calculate the distance from the point to the plane.
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Distance from point to plane formula
The following equation can be used to calculate the distance between a plane and a point.
d = \frac{|A\cdot X + B\cdot Y + C\cdot Z + D|}{\sqrt{A^2 + B^2 + C^2}}- Where d is the distance from the point to the plane
- A, B, C, and D are constants of the plane equation AX + BY + CZ + D = 0
- X, Y, and Z are the coordinates of the point
Distance From Point to Plane Definition
The distance from a point to a plane is defined as the shortest (perpendicular) distance from the point to the plane.
How to calculate the distance from a point to a plane?
How to calculate the distance from a point to a plane
- First, determine the equation of the plane.
A 3-dimensional plane can be represented using an equation in the form AX + BY + CZ + D = 0.
- Next, gather the constants from the equation in step 1.
Separate A, B, C, and D from the equation determined in step 1.
- Next, determine the coordinates of the point
Measure or calculate the coordinates of the point x, y, and z.
- Calculate the distance
Calculate the distance from the point to the plane using the equation above and information from steps 1-3.
FAQ
Even though a plane extends infinitely, the distance from a point to a plane is well-defined: it is the shortest (perpendicular) distance from the point to the plane. You can compute it using the formula d=|AX+BY+CZ+D|/√(A²+B²+C²) for a plane written as AX+BY+CZ+D=0.
