Single-nucleotide polymorphisms (SNPs) are often linked to critical phenotypes such as diseases or responses to vaccines, medications and environmental factors. However, the specific molecular mechanisms by which a causal SNP acts is usually not obvious. Changes in RNA secondary structure emerge as a possible explanation necessitating the development of methods to measure the impact of single-nucleotide variation on RNA structure. Despite the recognition of the importance of considering the changes in Boltzmann ensemble of RNA conformers in this context, a formal method to perform directly such comparison was lacking. Here, we solved this problem and designed an efficient method to compute the relative entropy between the Boltzmann ensembles of the native and a mutant structure. On the basis of this theoretical progress, we developed a software tool, remuRNA, and investigated examples of its application. Comparing the impact of common SNPs naturally occurring in populations with the impact of random point mutations, we found that structural changes introduced by common SNPs are smaller than those introduced by random point mutations. This suggests a natural selection against mutations that significantly change RNA structure and demonstrates, surprisingly, that randomly inserted point mutations provide inadequate estimation of random mutations effects. Subsequently, we applied remuRNA to determine which of the disease-associated non-coding SNPs are potentially related to RNA structural changes.