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`r_mu = f( "a" , "b" )`

Enter a value for all fields

The **Ellipse Mean Radius** calculator estimates* Ellipse* an average radius (**r _{μ}**) of an ellipse based on the semi-major (

**INSTRUCTIONS:** Enter the following:

- (
**a**) Semi-Major axis Ellipse. - (
**b**) Semi-Minor axis Ellipse.

**Ellipse Mean Radius (r):** The calculator returns the mean radius (**r _{μ}**) the same units as the axes.

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.

This formula uses the average of 200 measurements of the radius based on the definition of an ellipse:

` x^2/a^2 + y^2/b^2 = 1`

This algorithm computes the average of the radius based on 100 computations based on an x value from -a to a, where y is computed and 100 computations based on a y value from -b to b. For each, the distance from the origin is computed

`d = sqrt(x^2+ y^2)`

... and the arithematic mean is returned.

**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)