Enter axis lengths and calculate volume instantly. View steps, exports, samples, and live plotting tools. Built for study, validation, modeling, and quick reporting tasks.
The examples below use center-to-vertex distances a, b, and c.
| Case | a | b | c | Volume Formula | Volume |
|---|---|---|---|---|---|
| Example 1 | 2.00 | 3.00 | 4.00 | 4abc / 3 | 32.0000 |
| Example 2 | 5.00 | 5.00 | 5.00 | 4abc / 3 | 166.6667 |
| Example 3 | 1.50 | 2.50 | 3.50 | 4abc / 3 | 17.5000 |
| Example 4 | 6.00 | 4.00 | 2.00 | 4abc / 3 | 64.0000 |
This calculator uses the orthogonal octahedron model. The six vertices lie on the coordinate axes at ±a, ±b, and ±c.
If you know the full tip-to-tip axis lengths Lx, Ly, and Lz, then a = Lx/2, b = Ly/2, c = Lz/2, and the volume becomes:
V = Lx × Ly × Lz / 6
A rectangular octahedron is often handled as an orthogonal octahedron in applied geometry. This shape is useful when a model has three perpendicular characteristic lengths instead of one uniform radius. In that case, the volume depends on the product of the three semiaxes.
In measurement workflows, one common source of error is mixing full tip-to-tip lengths with center-to-vertex distances. This page supports both inputs, so the same calculator can be used for geometry problems, lab sketches, and engineering notes without reworking the raw data.
The derived values also help with interpretation. Surface area is relevant for exposure and coating estimates. Edge lengths help when the wireframe or strut model matters. Optional density adds a quick mass estimate from the same geometric input set.
It uses the orthogonal octahedron model. The six vertices sit on three perpendicular axes at distances ±a, ±b, and ±c from the center.
The solid can be split into eight congruent tetrahedra. Adding their volumes leads to the compact result V = 4abc / 3.
Use the mode selector first. Semiaxis mode expects center-to-vertex distances. Full-axis mode expects the complete tip-to-tip measurements.
Yes. Use one consistent length unit through the entire form. The calculator then reports area in squared units and volume in cubic units.
Density is optional. When entered, the calculator multiplies density by volume to estimate mass using the same chosen cubic length basis.
A general orthogonal octahedron is not regular. Edges connecting different axis pairs form three distinct length families: XY, XZ, and YZ.
The graph draws the solved octahedron in 3D using the resolved semiaxis values. It helps verify shape proportions before reporting results.
Yes. The page includes CSV export for tabular records and PDF export for quick summaries, reporting, or documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.