The hypothesis of universality implies that for every scaling relation among critical exponents there exists a universal ratio among the corresponding critical amplitudes. If one writes $B{|t|}^{\ensuremath{\beta}}$, ${{A}_{F}}^{\ifmmode\pm\else\textpm\fi{}}{|t|}^{2\ensuremath{-}\ensuremath{\alpha}}$, ${C}^{\ifmmode\pm\else\textpm\fi{}}{|t|}^{\ensuremath{-}\ensuremath{\gamma}}$, and ${\ensuremath{\xi}}_{0}{|t|}^{\ensuremath{-}\ensuremath{\nu}}$ [where $t=\frac{({p}_{c}\ensuremath{-}p)}{{p}_{c}}$, $p$ being the concentration of nonzero bonds, and +(-) stands for $pl{p}_{c}$ ($pg{p}_{c}$)] for the leading singular terms in the probability to belong to the infinite cluster, the mean number of clusters, the clusters' mean-square size, and the pair connectedness correlation length, then it is shown that the ratios $\frac{{{A}_{F}}^{+}}{{{A}_{F}}^{\ensuremath{-}}}$, $\frac{{C}^{+}}{{C}^{\ensuremath{-}}}$, ${{A}_{F}}^{+}{B}^{\ensuremath{-}2}{C}^{+}$, $\frac{{\ensuremath{\xi}}_{0}^{+}}{{\ensuremath{\xi}}_{0}^{\ensuremath{-}}}$, and ${{A}_{F}}^{+}{({\ensuremath{\xi}}_{0}^{+})}^{d}$ ($d$ is the dimensionality) are universal. Similar quantities are found for the behavior at $p={p}_{c}$ (as a function of a "ghost" field). All of these universal ratios are derived from a universal scaled equation of state, which is calculated to second order in $\ensuremath{\epsilon}=6\ensuremath{-}d$. The (extrapolated) results are compared with available information in dimensionalities $d=2, 3, 4, 5$, with reasonable agreements. The amplitude relations become exact at $d=6$, when logarithmic corrections appear. Additional universal ratios are obtained for the confluent correction to scaling terms.