  Using conformal field theory, we derive several new crossing formulas at the
two-dimensional percolation point. High-precision simulation confirms these
results. Integrating them gives a unified derivation of Cardy's formula for the
horizontal crossing probability $\Pi_h(r)$, Watts' formula for the
horizontal-vertical crossing probability $\Pi_{hv}(r)$, and Cardy's formula for
the expected number of clusters crossing horizontally $\mathcal{N}_h(r)$. The
main step in our approach implies the identification of the derivative of one
primary operator with another. We present operator identities that support this
idea and suggest the presence of additional symmetry in $c=0$ conformal field
theories.
