Ellipse Horizontal Chord from Edge

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The Ellipse Horizontal Chord from Edge calculator computes the chord of an ellipse where the chord is horizontal at a distance from the edge.

INSTRUCTIONS: Choose units and enter the following:

(A) Semi-Major Axis
(B) Semi-Minor Axis
(d) Vertical Distance from Edge

Ellipse Horizontal Chord from Edge (HE): The results are returned in centimeters. However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Ellipse Horizontal Chord from Edge equation computes the length of the horizontal chord in an ellipse that is a distance from the edge parallel to semi-major axis.

`HE = 2*(A/B) * sqrt(2*B*d-d*d)`

where:

HE = length of the horizontal chord
A = length of semi-major axis
B = length of semi-minor axis
d = vertical distance from the edge.

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.