What is an Ellipse?

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. In simpler terms, it is a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two fixed points (the foci) is constant. Our Ellipse Calculator Online helps you instantly find the geometric properties of this shape using the semi-major and semi-minor axes.

How to Use the Ellipse Calculator

Using this tool is straightforward. Simply follow these steps:

1. Enter the length of the Semi-major axis (a). This is half of the longest diameter.
2. Enter the length of the Semi-minor axis (b). This is half of the shortest diameter.
3. Click the "Calculate Properties" button to see the results.

Key Ellipse Formulas

This calculator utilizes standard geometric formulas to provide accurate results:

• Area: The area is calculated as π × a × b.
• Perimeter: Unlike a circle, the perimeter of an ellipse is difficult to calculate exactly. We use Ramanujan's second approximation, which is highly accurate.
• Eccentricity: This measures how "stretched" the ellipse is, calculated as √(1 - (b²/a²)).
• Linear Eccentricity (Foci): The distance from the center to each focus, found via √(a² - b²).

Frequently Asked Questions

Is an ellipse the same as an oval? While all ellipses are ovals, not all ovals are ellipses. An ellipse has a very specific mathematical definition based on its foci.

What happens if a and b are equal? If the semi-major and semi-minor axes are equal, the ellipse becomes a perfect circle with an eccentricity of 0.