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Elliptical Volume

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Last modified by
on
Aug 2, 2024, 7:20:49 PM
Created by
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Jun 7, 2018, 6:17:50 PM
V=π⋅a⋅b⋅h
(a)semi-major axis
(b)semi-minor axis
(h)height of the column

The Elliptical Volume calculator computes the volume of an ellipse shaped column using the semi-major (a) and semi-minor (b) axes and the height of the column (h).  Note: this is a different that the volume of an ellipsoid (see below)./attachments/163a2ed1-6a7f-11e8-abb7-bc764e2038f2/Elliptical Volume.png

INSTRUCTIONS:  Choose units and enter the following:

  • (a) semi-major axis
  • (b) semi-minor axis
  • (h) height of the column

Volume of Ellipse Shaped Column (V): The calculator returns the volume in cubic meters and the top surface area in square meters.  However these can be automatically converted to compatible units via the pull-down menu next to the resulting answer.

The Math / Science

An elliptical volume is a three dimension object with an elliptical base and top and vertical sides (see diagram above).  This differs from an ellipsoid which is a symmetric curved surface volume with elliptical cross-sections (see diagram below).  The formula for an elliptical volume is:

    V = π•a•b•h

where:

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. 

Ellipsoid Calculator

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  Elliptical columnComputes 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 and horizontal chords

Ellipse Chords

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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