How to use this calculator
- Identify the measurements labelled Side a. 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 = √3 a²/4; h = √3 a/2
Side a = 6
Worked example
For Side a = 6 cm, applying the displayed relationship gives side ≈ 6 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
An altitude bisects the opposite side and creates two 30–60–90 right triangles. The centroid, circumcentre, incentre and orthocentre coincide. The height is √3/2 times the side.
The altitude is shorter than the side. An arbitrary triangle cannot use these formulas merely because two sides look similar. 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.