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`e = sqrt(1 - (b^2/a^2))`

Enter a value for all fields

The **Eccentricity of an Ellipse** calculator computes the eccentricity of a conic section (e.g., ellipse) based on the lengths of the semi major and minor axes.

**INSTRUCTIONS**: Choose units and enter the following:

- (
**a**) semi-**major**axis (see diagram) - (
**b**) semi-**minor**axis (see diagram)

**Eccentricity (e):** The calculator returns the **eccentricity of the ellipse**.

In mathematics, an **ellipse** is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how "elongated" it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle to arbitrarily close to but less than 1.

The formula for the eccentricity of an ellipse is:

where:

- e = eccentricity
- a = length of the semi-major axis
- b = length of the semi-minor axis

- The eccentricity of a circle is zero, where a = b
- The eccentricity of an ellipse is from zero up to, but not including 1.
- The eccentricity of a parabola is 1.
- The eccentricity of a hyperbola is greater than one.

**Area of an Ellipse:**This computes the area of an ellipse based on the length of the axes.**Rumanujan's Circumference of an Ellipse 1:**This is the first of two of Rumanujan's approximations of the circumference (perimeter) of an ellipse based on the semi-major axis (**a**) and the semi-minor axis (**b**).**Rumanujan's Circumference of an Ellipse 2:**This is the second of Rumanujan approximations of the circumference (perimeter) of an ellipse based on the semi-major axis (**a**) and the semi-minor axis (**b**).**Circumference of an Ellipse (other)**This is another common estimation of the circumference (perimeter) of an ellipse based on the semi-major axis (**a**) and the semi-minor axis (**b**).**Eccentricity of an Ellipse:**This computes the eccentricity of an ellipse which is based on the ratios of the semi-major axis (**a**) and the semi-minor axis (**b**).**Mean Radius of an Ellipse:**This compute the mean radius of an ellipse. This would define a circle with the same approximate area, based on the ellipse's semi-major axis (**a**) and the semi-minor axis (**b**).**Linear Eccentricity of an Ellipse**: This computes the linear eccentricity of an ellipse.

Description of an ellipse is from Wikipedia (en.wikipedia.org/wiki/Ellipse)