  We present the calculation of thermal noise in interferometric
gravitational-wave detectors due to the thermal fluctuations of the beam
splitter (BS). This work makes use of a recently developed method of the
analysis of thermal noise in mirrors from first principles, based on the
fluctuation dissipation theorem. The evaluation of BS thermal noise is carried
out for the two different grav- itational wave observatories, GEO600 and the
Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO). The
analysis evaluates thermal noise from both the substrate and the optical
reflective and antireflective stacks located on the BS surface. We demonstrate
that the fluctuations of both reflecting and anti-reflecting surfaces
significantly contribute to the total thermal noise of the BS. The oscillating
intensity pattern couples small-scale distortions of the surface to the overall
phase readout, and therefore increases the overall thermal noise. In the case
of aLIGO, the BS contribution is with $0.3\%$ negligibly small. At a frequency
of 500Hz, the BS causes about $10\%$ of GEO600's sensitivity limit. BS noise
impairs the feasible sensitivity of the GEO-HF design proposal by about $50\%$.
