Tetrahedron Volume from Four Vertices Calculator
Calculate tetrahedron volume, triangular face areas and uniform-solid centroid from four 3D vertices.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Form three edge vectors from the first vertex and take their scalar triple product. Calculate each face area with a vector cross product.
Volume=|a·(b×c)|/6; triangle area=|u×v|/2; centroid=(A+B+C+D)/4
Worked example
The origin and three unit-axis endpoints form a tetrahedron of volume 1/6, centroid (1/4,1/4,1/4), and surface area (3+√3)/2.
Assumptions and input details
Exactly four Cartesian vertices, each coordinate magnitude at most 1e6, in one common length unit. Areas use its square and volumes its cube. Signed volume depends on vertex ordering; geometric volume is nonnegative. Coplanar or repeated vertices can give a degenerate zero-volume shape. The centroid assumes uniform solid density. Very nearly coplanar data can lose relative precision; a zero displayed volume is not a structural assessment.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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