We report on a simple mass formula for the relativistic bound state $Q\overline{Q}$ system which describes remarkably well the family of mesons ($\ensuremath{\rho}$,$\ensuremath{\omega}$,$\ensuremath{\varphi}$,$\frac{J}{\ensuremath{\psi}}$,$\ensuremath{\Upsilon}$;$\ensuremath{\pi}$,$K$,${K}^{*}$,$D$,${D}^{*}$,$F$,${F}^{*}$): ${M}^{2}={({m}_{1}+{m}_{2})}^{2}+[\frac{2{m}_{1}{m}_{2}}{({{m}_{1}}^{2}+{{m}_{2}}^{2})}]({m}_{1}+{m}_{2})\ensuremath{\Omega}(n+2)\ensuremath{-}\frac{c{({m}_{1}+{m}_{2})}^{2}}{({{m}_{1}}^{2}+{{m}^{2}}_{2})},$ where ${m}_{1}$,${m}_{2}$ are the constituent quark masses, $\ensuremath{\Omega}$ is a universal constant (= 0.6624 GeV), $n$ is the quantum number for the state, and $c$ is an effective constant which measures how far off-shell the quarks are in their bound state, i.e., $〈{{p}_{1}}^{2}+{{m}_{1}}^{2}+{{p}_{2}}^{2}+{{m}^{2}}_{2}〉=c\ifmmode\cdot\else\textperiodcentered\fi{}c$ depends weakly on the spin-triplet or singlet nature of the $Q\overline{Q}$ system. The parameters found in our fit are (in GeV units) ${m}_{u}={m}_{d}=0.83869$, ${m}_{s}=0.87988$, ${m}_{c}=1.50967$, ${m}_{b}=4.39312$, $c(\mathrm{triplet})=2.77690$, ${c}_{\ensuremath{\pi}}(\mathrm{singlet})=2.50840$, ${c}_{K}(\mathrm{singlet})=2.49276$. A derivation based on a parton picture of a constituent-bound-state system of $Q\overline{Q}$ is given. Implications of this mass formula for higher-mass states are discussed.