To calculate the eccentricity of a hyperbola, you need to know – at least – the major/minor semi-axis, a, and b.
The formula for the eccentricity of a hyperbola is, for both vertical and horizontal hyperbolas:
e = sqrt(1 + (b²/a²))
An extremely "flat" hyperbola has a high eccentricity, while a thin curve has an eccentricity of 1. Read more