Radiative transfer calculations for nadir-viewing satellites normally assume the atmosphere to be horizontally homogeneous. Yet it has been shown recently that horizontal gradients can lead to significant errors in satellite infrared and microwave soundings. We extend the methodology to nadir backscatter ultraviolet forward modeling and present a first estimate of the effect's magnitude. The Solar Backscatter Ultraviolet/2 (SBUV/2) instrument, a nadir sounder, serves as our test bed. We find that the RMS error in calculated SBUV radiance induced by ozone inhomogeneities ranges between 0.05 and 0.3% (0.1--0.5%) for the 318 nm (306 and 313 nm) channel. The lower (higher) estimate corresponds to soundings with small (high) solar zenith angle. Occurrence of higher errors, particularly at wavelengths longer than 300 nm, coincides with some of the most interesting atmospheric phenomena like tropopause folds and the south polar ozone hole. This leads to a seasonal variation of the magnitude of the effect. Because of the mostly zonal variability of the ozone distribution, there is also the possibility that biases may be introduced, which is particularly critical if the data are to be assimilated or used to determine trends. The results presented are tested for robustness using different model atmospheres.