Ellipse Axis Length

This Axis of an Ellipse calculator approximates  one axis of an ellipse based on the circumference and other axis of an ellipse.  

INSTRUCTIONS:  Choose units and enter the following parameters;

• (C) Circumference of Ellipse
• (b) Length of the semi-minor axis (see diagram)

Axis of Ellipse(a): The calculator returns the length of the axis in meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

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.   The formula for the circumference of an ellipse used in this calculator is:

      `C =2pi sqrt((a^2 + b^2)/2`

If we solve for an the length of an axis (a), the formula for the length of an ellipse axis based on the circumference and other axis is: Conic Sections

      `a = sqrt(c^2/(2*pi^2) - b^2)`

where:

• a = length of ellipse axis
• C = circumference of ellipse
• b = length of other ellipse axis

Note: their is no weighting on whether an axis is the major or minor axis. 

Ellipse Calculators

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 Chords

• 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 (3D Elliptical Shape)

• 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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Reference

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