  We give various formulas to compute the number of all involutions, i.e.
elements of order 2, in an incidence algebra $I(X,\mathbb{K})$, where $X$ is a
finite poset (star, Y and Rhombuses) and $\mathbb{K}$ is a finite field of
characteristic different from 2. Using the techniques describing here we show
an algorithm to calculate the number of involutions on any finite poset.
