Residual stress in ceramics induced by grinding plays an important role on the strength of ceramics. The X-ray method is effective in measuring residual stress in ceramics because it can nondestructively measure the residual stress in thin surface layer of 10 to 40μm of a specimen. In the measurement by X-ray diffraction, it is important to ascertain the reproducibility of the measured values from their standard deviation because the measurements by X-rays will involve variability caused by inherent counting statistics. To determine accurately the stress value in a sintered silicon carbide, an X-ray stress constant and elastic constants were determined by the Gaussian curve method which permits rapid and precise determination of stress. The standard deviations of these constants were calculated analytically to examine their reliability. (2.0.15) and (306) diffraction planes of silicon carbide were measured with CuKα radiation. For each diffraction plane, CuKα1, and Kα2 diffraction line profiles appear separately. Stress can be determined precisely by using the separate Kα1 single diffraction profile. The background correction in determining peak positions can be omitted because it does not affect the stress. The 95% confidence limits for the X-ray stress constants for the (2.0.15) and (306) planes were -971±48 and -1337±116MPa/deg, respectively. The limits for the X-ray Young's modulus of the (2.0.15) and (306) planes were 446±20 and 417±35GPa, and those for the Poisson's ratio were 0.165±0.013 and 0.157±0.016, respectively.