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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.

An ellipse is defined by the semi-major axis (**A**) and semi-minor axis (**B**).

**Area of Ellipse:**Computes the area of an ellipse based on the semi-major axis (**a**) and the semi-minor axis (**b**).**Rumanujan's Circumference of an Ellipse 1**: 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:**The second 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)**Another common estimation of the circumference (perimeter) of an ellipse based on the semi-major axis (**a**) and the semi-minor axis (**b**).**Ellipse Axis Length**: Approximates one axis of an ellipse bases on the circumference and the other axis.**Eccentricity of an Ellipse**Computes the eccentricity of an ellipse which is based on the ratios of the semi-major axis (**a**) and the semi-minor axis (**b**).**Linear Eccentricity of an Ellipse (f)**Computes the distance from the center to either foci (**f**), which is the linear eccentricity of an ellipse. This is based on the semi-major axis (**a**) and the semi-minor axis (**b**).**Mean Radius of an Ellipse**Computes 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**).**Elliptical Volume**Computes the volume of a column with an elliptical base.

**Ellipse Vertical Chord from Edge (VE):**Computes the length of the vertical chord of an ellipse based on distance from the edge.**Ellipse Vertical Chord from Center (VC):**Computes the length of the vertical chord of an ellipse based on distance from the center.**Ellipse Horizontal Chord from Edge (HE):**Computes the length of the horizontal chord of an ellipse based on distance from the edge.**Ellipse Horizontal Chord from Center (HC)**: Computes the length of the vertical chord of an ellipse based on distance from the center.

**Ellipsoid - Volume**computes the volume of an ellipsoid based on the length of the three semi-axes (a, b, c)**Ellipsoid - Surface Area**computes the surface area of an ellipsoid based on the length of the three semi-axes (a, b, c)**Ellipsoid - Mass or Weight**computes the mass or weight of an ellipsoid based on the length of the three semi-axes (a, b, c) and the mean density.

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