A new method is developed to estimate the contemporary effective population size (Ne) from linkage disequilibrium between SNPs without information on their location, which is the usual scenario in non-model species. The general theory of linkage disequilibrium is extended to include the contribution of full-sibs to the measure of LD, leading naturally to the estimation of Ne in monogamous and polygamous mating systems, as well as in multiparous species, and non-random distributions of full-sib family size due to selection or other causes. The prediction of confidence intervals for Ne estimates was solved using a small artificial neural network trained on a dataset of over 105 simulation results. The method, implemented in a user-friendly and fast software (currentNe) is able to estimate Ne even in problematic scenarios with large population sizes or small sample sizes, and provides confidence intervals that are more consistent than parametric methods or resampling.