How to use this calculator
- Identify the measurements labelled Base b, 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 = √(h²+b²/4)
Base b = 6; Height h = 4
Worked example
For Base b = 6 cm, Height h = 4 cm, applying the displayed relationship gives equal side ≈ 5 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
The altitude from the vertex between the equal sides bisects the base and the vertex angle. The two base angles are equal. A non-degenerate triangle requires b < 2a.
Vertex angle means the angle between the equal sides. The base is not necessarily the longest side. 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.