The Stoney formula, based on the measurement of the substrate curvature, is often used for the determination of the thin films' residual stress. In this study, titanium nitride coatings were deposited by DC reactive magnetron sputtering on silicon substrates. An optical profiler was used to determine the curvature of the surface before and after coating. Two radii were then obtained, along the principal perpendicular directions of the surface curvature. A simple and efficient method to determine the experimental error on the stress calculation was developed taking into account the film thickness dispersion and the radii dispersion. Using constant deposition parameters, some samples' characteristics were tested: film and substrate thickness, size, shape and crystallographic orientations of the substrates. With the help of the developed error method, we analyzed what can be conclude about the influence of these characteristics on the calculated stress values, obtained from the experimental measurements.