The ellipse area calculator will help you determine the area of an ellipse. In the article below, you will find more about the tool and some additional information about the area of an oval, including the ellipse area formula. Read on if you want to learn about the ellipse definition, the foci of an ellipse, and discover what's the ellipse equation. And if you already know all the basics and are looking for something more complicated than this oval area calculator, check out our advanced ellipse calculator.

What is an ellipse? Ellipse definition

ellipse
Credit: Wikimedia.org

An ellipse is an oval shape, resembling a squashed circle. It's a generalized case of a closed conical section, which means that you obtain it by slicing a cone with an inclined plane. If the the inclination angle equals zero, you get a circle. In fact, circles are a subset of an ellipse!

While talking about the ellipse definition, it's important to mention the ellipse equation, which is as follows (please note that this is not the ellipse area formula!):

(xc1)2a2+(yc2)2b2=1\frac{(x-c_1)^2}{a^2}+\frac{(y-c_2)^2}{b^2}=1

where:

  • (x,y)(x, y) – Coordinates of an arbitrary point on the ellipse;
  • (c1,c2)(c_1, c_2) – Coordinates of the ellipse's center;
  • aa – Distance between the center and the ellipse's vertex, lying on the horizontal axis; and
  • bb – Distance between the center and the ellipse's vertex, lying on the vertical axis.

🙋 If you are interested in other figures you obtain by slicing a cone, visit our Conic sections calculator!

What are the foci of an ellipse?

The foci of an ellipse are two points that lie on its longest axis, equidistant from the ellipse's center on each side. You need to determine them if you want to draw an oval. The foci on an ellipse definition are the set of all points for which the sum of distances to the first and second focus is equal to a constant value.

In the image above, the foci are points F1F_1 and F2F_2.

How to use the ellipse area calculator?

To calculate the area of an oval using our calculator, you only need to do two things:

  1. Input the YY value.
  2. Input the XX value.
  3. Find the result in the bottom-most field of the ellipse area calculator.

How to calculate the area of an ellipse?

But how does it work? The ellipse area formula is much shorter than the general ellipse equation:

areaellipse=π×X×Y\mathrm{area_{ellipse}} = \pi\times X\times Y

where:

  • XX – Distance between the center of the ellipse and a vertex; and
  • YY – Distance between the ellipse center and a co-vertex.

You can see which distances they are in the illustration above the oval area calculator.

Other geometry calculators you might find useful

If you need to calculate the areas, perimeters, or different parameters of shapes other than an ellipse, you might find some of our geometry calculators helpful. They include:

Visit our 2D geometry section to see all the calculators we have to offer.

Maria Kluziak
Ellipse area calculator: ellipse
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