How to use this calculator
- Identify the measurements labelled Height h. 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
a = h√(3/2)
Height h = 4.8989794856
Worked example
For Height h = 4.8989794856 cm, applying the displayed relationship gives edge ≈ 6 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Its height is a√(2/3), its surface area is √3a², and its volume is a³/(6√2). The altitude reaches the centre of the opposite equilateral face.
These formulas require all six edges to be equal. A face altitude and the solid’s vertical height are different. 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.