THE FEUTEX TOOLKIT

Tetrahedron Volume from Edge Vectors

Compute the volume and orientation of a tetrahedron from its three shared-origin edge vectors.

Geometry workspace● Runs in your browser

01 Your input

Edge A xlengthEdge A ylengthEdge A zlengthEdge B xlengthEdge B ylengthEdge B zlengthEdge C xlengthEdge C ylengthEdge C zlength

02 Your result

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Result data

Formula

Signed Volume = (ax*(by*cz-bz*cy)-ay*(bx*cz-bz*cx)+az*(bx*cy-by*cx))/6; Volume = abs(ax*(by*cz-bz*cy)-ay*(bx*cz-bz*cx)+az*(bx*cy-by*cx))/6

Sources and model references

Made for real tasks

Compute the volume and orientation of a tetrahedron from its three shared-origin edge vectors.

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

Enter edge a x, edge a y, edge a z, edge b x, edge b y, edge b z, edge c x, edge c y, edge c z.
Use the displayed units and confirm the model assumptions.
Calculate and compare the outputs against your input scenario.

{
  "ax": 3,
  "ay": 0,
  "az": 0,
  "bx": 0,
  "by": 4,
  "bz": 0,
  "cx": 0,
  "cy": 0,
  "cz": 5
}

Vectors must start at the same vertex; zero volume means coplanar points.

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.