How to use this calculator
- Identify the measurements labelled Semi-major axis a, Eccentricity e. 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
Semi-major axis a = 6; Eccentricity e = 0.6
Worked example
For Semi-major axis a = 6 cm, Eccentricity e = 0.6, applying the displayed relationship gives area ≈ 90.477868 cm². The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Area is exactly πab in the mathematical model. Eccentricity is √(1−b²/a²), and ranges from zero for a circle to values approaching one for very elongated ellipses. The perimeter does not have a simple elementary formula.
Semi-axes are half the full axis lengths. The approximation label applies to perimeter, not to the area formula. 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.