Enter the two semi-axis lengths to calculate ellipse area and a Ramanujan perimeter approximation.
Ellipse circumference has no elementary closed form; this uses Ramanujan's highly accurate approximation.
Calculate ellipse area, perimeter approximation, eccentricity, foci, latus rectum and a scaled verification diagram.
Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
Ellipse formulas normally use semi-major axis a and semi-minor axis b. If a drawing provides the full major and minor diameters, divide each by two before entering the values or the area will be four times too large.
The focal distance formula c = sqrt(a² − b²) assumes a is the semi-major axis. If the entered values are reversed, swap their roles before interpreting eccentricity or focus locations even though the area πab is unchanged.
Unlike circumference of a circle, ellipse perimeter has no simple elementary closed form. Compare the displayed approximation with limiting cases: when a and b are equal it should approach 2πa, and highly stretched ellipses should reflect the longer axis strongly.
Two ellipses with proportional semi-axes have the same eccentricity even if one is physically much larger. Use area or axis lengths for scale and eccentricity for how far the shape departs from a circle.
For any point on an ideal ellipse, the sum of distances to the two foci is constant and equals 2a. Checking one or more plotted points against that relationship is an independent way to catch an axis or focus calculation error.
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