Hyperbola Eccentricity Calculator

Visualize and understand hyperbola shapes by calculating eccentricity.

Enter semi-transverse axis (a) and semi-conjugate axis (b) to calculate.

Semi-Transverse Axis (a)

Distance from center to vertex along the transverse axis.

Semi-Conjugate Axis (b)

Distance from center to co-vertex along the conjugate axis.

Eccentricity (e):

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

Hyperbola Visualization

Understanding Hyperbola Eccentricity

Eccentricity (e) is a key characteristic of a hyperbola that tells us how "open" or "wide" it is. It's always a number greater than 1. A larger eccentricity means the hyperbola opens wider, approaching two straight lines. As eccentricity gets closer to 1, the hyperbola becomes narrower, more pointed around its vertices.

The formula to calculate eccentricity (e) is: $$e = \sqrt{1 + \frac{b^2}{a^2}}$$, where 'a' is the semi-transverse axis (horizontal axis in standard orientation) and 'b' is the semi-conjugate axis (vertical related axis).

This calculator simplifies finding the eccentricity by just requiring the values of 'a' and 'b'. The visualization helps to see how the calculated eccentricity relates to the shape of the hyperbola.