  Cell shape is fundamental in biology. The average cell shape can influence
crucial biological functions, such as cell fate and division orientation. But
cell-to-cell shape variability is often regarded as noise. In contrast, recent
works reveal that shape variability in diverse epithelial monolayers follows a
nearly universal distribution. However, the origin and implications of this
universality are unclear. Here, assuming contractility and adhesion are crucial
for cell shape, characterized via aspect ratio (AR), we develop a mean-field
analytical theory for shape variability. We find that a single parameter,
$\alpha$, containing all the system-specific details, describes the probability
distribution function (PDF) of AR; this leads to a universal relation between
the standard deviation and the average of AR. The PDF for the scaled AR is not
strictly but almost universal. The functional form is not related to jamming,
contrary to common beliefs, but a consequence of a mathematical property. In
addition, we obtain the scaled area distribution, described by the parameter
$\mu$. We show that $\alpha$ and $\mu$ together can distinguish the effects of
changing physical conditions, such as maturation, on different system
properties. The theory is verified in simulations of two distinct models of
epithelial monolayers and agrees well with existing experiments. We demonstrate
that in a confluent monolayer, average shape determines both the shape
variability and dynamics. Our results imply the cell shape variability is
inevitable, where a single parameter describes both statics and dynamics and
provides a framework to analyze and compare diverse epithelial systems.
