What is the diameter of an ellipse

Calculate ellipse

The ellipse is a flat geometric shape with no corners. The elliptical line includes all points on a plane whose sum of the distances to two given points, the so-called focal points, is equal to a given value. This value is twice the major semi-axis or corresponds to the largest diameter of the ellipse.

The distance between the focal points and the center of the ellipse is called linear eccentricity, which means that it is always in the interval between 0 and the length of the major semi-axis. The quotient of the linear eccentricity and the major semi-axis is called numerical eccentricity, which is therefore in the range from 0 to 1. If the eccentricity is 0, it is a special ellipse, namely a circle. the greater the eccentricity, the more the ellipse deviates from the circular shape. The ellipse can therefore also be viewed as a compressed circle.

Large and small semiaxis, linear and numerical eccentricity, circumference and area of ​​an ellipse are partly mutually dependent. You can use this online calculator to calculate all of these sizes. In addition to the large or small semi-axis, you can specify any other size, or of course both semi-axes. The other input fields remain empty.

This elliptical calculator thus includes several computers in one, as two of the six variables can be specified and the other four variables are calculated. Certain combinations of values ​​in connection with a given circumference or a given area can lead to the major semi-axis turning out to be a small semi-axis or vice versa. In this case, the two semi-axes are swapped so that the greater length always represents the major semi-axis.

Decimal places are also taken into account for all entries. The result is output with a selectable precision from zero to six decimal places (Nkst.). Decimal places can be entered either with a comma or with a period.

With regard to the scope, it should be mentioned that this cannot be calculated exactly, but only approximately. The calculation of the circumference is more accurate the smaller the eccentricity, i.e. the more circular the ellipse is. This elliptical calculator uses the Ramanujan approximation formula, which delivers fairly accurate results and even in the worst case, i.e. a numerical eccentricity of 1, only has a relative error of a maximum of approx.

If the semi-axes are the same length, you can use the circle calculator.

If you like the possibilities of this calculator, you may also be interested in the calculators for other flat, geometric shapes or three-dimensional bodies.

Please also note our explanations on the accuracy of results and the representation of numbers.