Ellipse Eccentricity Calculator

Discover the shape of an ellipse by calculating its eccentricity. Enter the semi-major and semi-minor axes to visualize and understand.

Ellipse Parameters

Define the ellipse by entering its semi-major and semi-minor axes.

Semi-Major Axis (a)

units

Semi-Minor Axis (b)

units

Eccentricity Result

Eccentricity (e):

Formula: $$ e = \sqrt{1 - \frac{b^2}{a^2}} $$

Visualize Ellipse

Understanding Ellipse Eccentricity

Eccentricity measures how much an ellipse deviates from a perfect circle. It's a value between 0 and just under 1. An eccentricity of 0 is a circle, and values closer to 1 are more elongated ellipses.

The formula for eccentricity (e) is: $$ e = \sqrt{1 - \frac{b^2}{a^2}} $$, where 'a' is the semi-major axis (longest radius) and 'b' is the semi-minor axis (shortest radius).

Semi-major axis (a): Longest radius from the center to the ellipse edge.
Semi-minor axis (b): Shortest radius from the center to the ellipse edge.
Eccentricity (e): Shape descriptor, 0 for circle, closer to 1 for elongated ellipse.
Foci: Two points inside the ellipse used in its definition. Plotted as red dots in the visualization.

For deeper insights, visit Wikipedia on Ellipses.