Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Plane Angle and Intersection Direction

Find the acute angle between planes and a direction vector for their intersection line.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaAcute Angle = acos(min(1,abs(a1*a2+b1*b2+c1*c2)/(hypot(a1,b1,c1)*hypot(a2,b2,c2)))); Direction X = b1*c2-c1*b2; Direction Y = c1*a2-a1*c2; Direction Z = a1*b2-b1*a2
Sources and model references

Worked example

Inputs

A1
1 number
B1
0 number
C1
0 number
A2
0 number
B2
1 number
C2
0 number

Expected results

Acute Angle
1.570796327 rad
Direction X
0 number
Direction Y
0 number
Direction Z
1 number

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

How to use this tool

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

Try this example

{
  "a1": 1,
  "b1": 0,
  "c1": 0,
  "a2": 0,
  "b2": 1,
  "c2": 0
}

Accuracy and scope

Zero intersection direction means parallel planes; offsets are not considered. 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.