Elipse — Excentricidade

The ellipse eccentricity calculator determines how elongated an ellipse is by measuring its deviation from a perfect circle. Eccentricity (e) is a number between 0 and 1, where 0 represents a circle and values close to 1 indicate a very elongated ellipse. To calculate, you need the lengths of the semi-major axis (a) and semi-minor axis (b). The formula used is e = √(1 − b²/a²), which directly relates the difference between the axes.

Practical use of this calculator is common in fields such as astronomy, engineering, and physics. For example, when studying planetary orbits, eccentricity determines the shape of a celestial body's trajectory. The higher the eccentricity, the more eccentric the orbit. It is also useful in designing elliptical mirrors, parabolic antennas, and lenses, where the precise shape of the ellipse is essential for performance.

Be careful when entering the axis values. The semi-major axis (a) must always be greater than or equal to the semi-minor axis (b). If you swap them, the result may be incorrect or even a square root of a negative number, which is invalid. Also, ensure that the units of measurement are consistent; eccentricity is dimensionless, so it doesn't matter if you use meters or centimeters, as long as both are in the same unit.

Another caution: the calculator assumes the ellipse is centered at the origin and that the axes are aligned with the coordinate axes. Otherwise, the eccentricity remains the same, but the formula applies similarly. Remember that eccentricity does not depend on the orientation of the ellipse, only on the relationship between the axes.