THE FEUTEX TOOLKIT

Point Projection onto a Plane

Project a three-dimensional point onto a plane and measure its perpendicular distance.

Geometry workspace● Runs in your browser

01 Your input

AnumberBnumberCnumberDnumberXlengthYlengthZlength

02 Your result

View or copy raw result data

Result data

Formula

Distance = abs(a*x+b*y+c*z+d)/hypot(a,b,c); Foot X = x-a*(a*x+b*y+c*z+d)/(a**2+b**2+c**2); Foot Y = y-b*(a*x+b*y+c*z+d)/(a**2+b**2+c**2); Foot Z = z-c*(a*x+b*y+c*z+d)/(a**2+b**2+c**2)

Sources and model references

https://mathworld.wolfram.com/Point-PlaneDistance.html

Worked example

Inputs

A: 0 number
B: 0 number
C: 1 number
D: -2 number
X: 3 length
Y: 4 length
Z: 7 length

Expected results

Distance: 5 length
Foot X: 3 length
Foot Y: 4 length
Foot Z: 2 length

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "a": 0,
  "b": 0,
  "c": 1,
  "d": -2,
  "x": 3,
  "y": 4,
  "z": 7
}

Accuracy and scope

Plane convention: ax + by + cz + d = 0. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.