How to use this calculator
- Identify the measurements labelled Space diagonal d, Length a, Width b. 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 = 10; Length a = 6; Width b = 5
Worked example
For Space diagonal d = 10 cm, Length a = 6 cm, Width b = 5 cm, applying the displayed relationship gives length ≈ 6 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Opposite faces are congruent. The space diagonal connects opposite vertices through the interior and is √(a²+b²+c²). Total surface area includes each of the three distinct face areas twice.
Internal capacity and external dimensions differ for a box with thick walls. Choose one consistent measurement convention. 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.