Super-resolution is a technique that produces higher resolution images from low resolution images (LRIs). In practice, people have found that the improvement in resolution is limited. The aim of this paper is to address the problem "do fundamental limits exist for super-resolution?". Specifically, this paper provides explicit limits for a major class of super-resolution algorithms, called the reconstruction-based algorithms, under both real and synthetic conditions. Our analysis is based on perturbation theory of linear systems. We also show that a sufficient number of LRIs can be determined to reach the limit. Both real and synthetic experiments are carried out to verify our analysis.