Description
Return their product divided by three.
Solid-geometry formulas assume particular shapes and measurement directions. Axial height, slant length, filled-volume centroid, and surface centroid are different quantities even when they describe the same object.
Return their product divided by three.
When to use this tool
Use Tetrahedron Face Altitude Volume Term when you need a local dimension, area, or centroid term for the stated ideal solid.
How to use the tool and how it works
- Enter faceArea, altitude. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read volume. Use the output convention below.
Require nonnegative faceArea and altitude. Return their product divided by three.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| faceArea | Face Area | Required. Finite number; minimum 0. |
| altitude | Altitude | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| volume | Volume | Required. Finite number. |
{
"input": {
"faceArea": 6,
"altitude": 4
},
"output": {
"volume": 8
}
}Limitations and assumptions
- Altitude is perpendicular distance to the face plane and units must give cubic length; no tetrahedron geometry, actual altitude, orientation, or nondegeneracy is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete solid model for clipping, oblique shapes, or nonuniform material. Confirm radius, height, and centroid conventions before applying an ideal-shape identity.
References
Similar or alternative tools
- Tetrahedron Face Normal Orientation
Cross B-A with C-A, dot with opposite-A, reverse the normal only for a positive dot, and return signedDot, outwardNormal, and degenerate for exact zero.
- Tetrahedron Oriented Volume Single Term
Return coordinate × cofactor/6 as volumeContribution.