How to use this calculator
- Identify the measurements labelled Space diagonal d. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
Space diagonal d = 8.6602540378
Worked example
For Space diagonal d = 8.6602540378 cm, applying the displayed relationship gives edge ≈ 5 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Its face diagonal is a√2 and its space diagonal is a√3. Total surface area counts all six faces. Volume counts the enclosed three-dimensional space and therefore uses cubic units.
A face diagonal and a space diagonal are different measurements. Surface area is not measured in cubic units. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.