Tetrahedral Volume from Vertex Coordinates
In geometry, tetrahedra are 3-dimensional solids that have 4 vertices, 6 edges, and 4 triangular faces. They are also known as "triangular pyramids;" in their natural orientation they have a triangular base and 3 triangular sides that meet at a point.
If you know the coordinates of the vertices of a tetrahedron, you can compute its volume with a matrix formula.
You can also use the convenient volume calculator on the left. Simply enter the coordinates of four vertices in any order and click the "Find Volume" button.
The Matrix FormulaCall the four vertices of the tetrahedron (a, b, c), (d, e, f), (g, h, i), and (p, q, r). Now create a 4-by-4 matrix in which the coordinate triples form the columns of the matrix, with a row of 1's appended at the bottom:
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