What eccentricity value ($e$) defines a perfectly circular orbit?

A value of exactly zero ($e=0$)

Eccentricity ($e$) is the unitless parameter that quantifies the degree to which an orbit deviates from a perfect circle. Mathematically, a perfectly circular orbit is the specific case where the two foci perfectly overlap, meaning the distance from the center to a focus ($c$) is zero. Since eccentricity is calculated as the ratio of the distance from the center to a focus divided by the semi-major axis ($e = c/a$), if $c$ is zero, the resulting eccentricity must be exactly zero. As the eccentricity increases above zero, the ellipse becomes progressively more elongated or stretched out. Conversely, any orbit with $e>0$ is intrinsically elliptical, even if the deviation from a circle is minimal, as is the case with Earth's orbit ($e \approx 0.0167$).