We present an evaluation of heavy quarkonium states $b\overline{b}$, $c\overline{c}$ from first principles. We use tree-level QCD (including relativistic corrections) and the full one-loop potential; nonperturbative effects are taken into account at the leading order through the contribution of the gluon condensate $〈{\ensuremath{\alpha}}_{s}{G}^{2}〉$. We use the values $\ensuremath{\Lambda}(2\mathrm{loops},4\mathrm{flavors})={200}_{\ensuremath{-}60}^{+80}$ MeV, $〈{\ensuremath{\alpha}}_{s}{G}^{2}〉=0.042\ifmmode\pm\else\textpm\fi{}0.020{\mathrm{GeV}}^{4}$, but we trade the value of the quark mass with the masses of $\frac{J}{\ensuremath{\psi}}$, $\ensuremath{\Upsilon}$ as input. We get good agreement in what is essentially a zero parameter evaluation for the masses of the $1S$, $2S$, $2P$ states of $b\overline{b}$, the $1S$ state for $c\overline{c}$, and the decay $\ensuremath{\Upsilon}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$. As outstanding results we obtain the precise determination of ${m}_{b}$ as well as an estimate of the hyperfine splitting $M(\ensuremath{\Upsilon})\ensuremath{-}M({\ensuremath{\eta}}_{b}):{\overline{m}}_{b}({\overline{m}}_{b}^{2})={4397}_{\ensuremath{-}2}^{+7}{(\ensuremath{\Lambda})}_{+4}^{\ensuremath{-}3}{(〈{\ensuremath{\alpha}}_{s}{G}^{2}〉)}_{\ensuremath{-}32}^{+16}(\mathrm{syst})$ MeV, $M(\ensuremath{\Upsilon})\ensuremath{-}M({\ensuremath{\eta}}_{b})={36}_{\ensuremath{-}7}^{+13}{(\ensuremath{\Lambda})}_{\ensuremath{-}6}^{+3}{(〈{\ensuremath{\alpha}}_{s}{G}^{2}〉)}_{\ensuremath{-}5}^{+11}(\mathrm{syst})$ MeV, the first error due to that in $\ensuremath{\Lambda}$, the second to that in $〈{\ensuremath{\alpha}}_{s}{G}^{2}〉$ (varied independently). For the $c$ quark, we find ${\overline{m}}_{c}({\overline{m}}_{c}^{2})={1306}_{\ensuremath{-}34}^{+21}{(\ensuremath{\Lambda})}_{+6}^{\ensuremath{-}6}(〈{\ensuremath{\alpha}}_{s}{G}^{2}〉)$ MeV (up to systematic errors). The $\stackrel{-}{\mathrm{MS}} b$, $c$ masses correspond to pole mass values of ${m}_{b}(\mathrm{pole})={4906}_{\ensuremath{-}51}^{+69}{(\ensuremath{\Lambda})}_{+4}^{\ensuremath{-}4}{(〈{\ensuremath{\alpha}}_{s}{G}^{2}〉)}_{\ensuremath{-}40}^{+11}(\mathrm{syst})$ MeV and ${m}_{c}(\mathrm{pole})={1570}_{\ensuremath{-}19}^{+19}{(\ensuremath{\Lambda})}_{+7}^{\ensuremath{-}7}(〈{\ensuremath{\alpha}}_{s}{G}^{2}〉)$ MeV.