The concept of the relative biological effectiveness (RBE) is essential for treatment planning in carbon ion therapy and for understanding the biological effects of high-LET radiation. As this quantity depends on many factors, both its experimental determination and the assessment of its uncertainty are not trivial. For the limiting case of zero dose, where the RBE takes its maximum value RBE(alpha), we present in this article a simple empirical-based approach to estimate its uncertainty. A Gaussian error calculus is applied to equally take into account both uncertainties from experiments with high- and low-LET radiation. From a theoretical point of view, we then infer, using a simple Monte Carlo model, the distribution of RBE(alpha) values. This illustrates why the conventional error propagation approach is inappropriate in some cases. In these cases, likewise also the error estimates have to be obtained with a more sophisticated approach. Uncertainties of RBE, visualized by error bars, are of importance for treatment planning and also for setting up a precision goal for predicting biophysical models such as the local effect model.