Hipérbole — Excentricidade
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
e = √(1 + b²/a²)
About this calculator
The hyperbola eccentricity calculator computes the value of e from the semi-axes a and b. Eccentricity measures how elongated the hyperbola is, always greater than 1. The larger the value, the more open the curve. This tool is useful for students and professionals working with analytic geometry.
To use, enter the values of semi-axes a and b (both positive). The formula e = √(1 + b²/a²) is applied automatically. The result indicates the shape: values near 1 correspond to tighter hyperbolas, while larger values indicate more open curves.
This calculator is ideal for solving analytic geometry exercises, checking problem results, or understanding the relationship between hyperbola parameters. It can also be used in engineering and physics applications where hyperbolas appear, such as orbits and navigation systems.
Caution: ensure a and b are positive. Eccentricity is always greater than 1 for hyperbolas; if the result is 1 or less, review the values. Remember that the hyperbola has two branches, but the eccentricity is the same for both.
Frequently asked questions
What does eccentricity greater than 1 mean?
It means the curve is a hyperbola. The larger the value, the more elongated and open the hyperbola.
Can I use negative values for a or b?
No, semi-axes a and b must be positive. They represent distances in the Cartesian plane.
What is the difference between ellipse and hyperbola eccentricity?
For an ellipse, eccentricity is between 0 and 1; for a hyperbola, it is always greater than 1.
What happens if a is much larger than b?
The eccentricity approaches 1, resulting in a tighter hyperbola.
Does this calculator work for hyperbolas centered at the origin?
Yes, the formula assumes the hyperbola is centered at the origin and aligned with the coordinate axes.