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`C = pi * [3* ( "a" + "b" ) - sqrt((3* "a" + "b" ) ( "a" +3* "b" ))]`

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Rumanujan's **Circumference of an Ellipse** calculator approximates the circumference of an ellipse based on one of Rumanujan's approximations.

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

- (a) Length of the semi-major axis
- (b) Length of the semi-minor axis

**Circumference of an Ellipse (C):** The calculator returns the **circumference or perimeter of the ellipse** in meters. However, this can be automatically converted to compatible length units via the pull-down menu.

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 circumference of an ellipse has been approximated in several simple formulae including this one by the famous mathematician Rumanujan. The the formula for the circumference of an ellipse used in this calculator is:

`C = pi * [3* (a+b) - sqrt((3*a+b) (a+3*b))]`

where:

- C = circumference of ellipse
- a = length of semi-major axis
- b = length of semi-minor axis

**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**).*Conic Sections***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)