High-Reynolds-number turbulence driven by stellar convection in main-sequence stars generates stochastic gravitational radiation . We calculate the wave-strain power spectral density as a function of the zero-age main-sequence mass for an individual star and for an isotropic , universal stellar population described by the Salpeter initial mass function and redshift-dependent Hopkins-Beacom star formation rate . The spectrum is a broken power law , which peaks near the turnover frequency of the largest turbulent eddies . The signal from the Sun dominates the universal background . For the Sun , the far-zone power spectral density peaks at S ( f _ { \mathrm { peak } } ) = 5.2 \times 10 ^ { -52 } ~ { } \mathrm { Hz } ^ { -1 } at frequency f _ { \mathrm { peak } } = 2.3 \times 10 ^ { -7 } ~ { } \mathrm { Hz } . However , at low observing frequencies f < 3 \times 10 ^ { -4 } ~ { } \mathrm { Hz } , the Earth lies inside the Sun ’ s near zone and the signal is amplified to S _ { \mathrm { near } } ( f _ { \mathrm { peak } } ) = 4.1 \times 10 ^ { -27 } ~ { } \mathrm { Hz } ^ { -1 } because the wave strain scales more steeply with distance ( \propto d ^ { -5 } ) in the near zone than in the far zone ( \propto d ^ { -1 } ) . Hence the Solar signal may prove relevant for pulsar timing arrays . Other individual sources and the universal background fall well below the projected sensitivities of the Laser Interferometer Space Antenna and next-generation pulsar timing arrays . Stellar convection sets a fundamental noise floor for more sensitive stochastic gravitational-wave experiments in the more distant future .