Abstract Background This paper analyses the resolution achieved in localisation microscopy experiments. The resolution is an essential metric for the correct interpretation of super-resolution images, but it varies between specimens due to different localisation precisions and densities. Methods By analysing localisation microscopy as a statistical method of Density Estimation, we present a method that produces a blind estimate of the resolution in a super-resolved image. This estimate is derived directly from the raw image data without the need for comparisons with known calibration specimens. It is corroborated with simulated and experimental data. Results and discussion Localisation microscopy has a resolution limit equal to 2σ, where σ is the r.m.s. localisation precision, evaluated as an average Thompson precision, Cramer Rao bound, or otherwise. Further, for a limited-sampling case in which there is only one localisation per fluorophore, the expected resolution of an optimised super-resolution image is worsened to approximately 3σ, due to smoothing processes that are necessarily involved in visualising the specimen with limited data. This 2σ or 3σ resolution can be estimated for any localisation microscopy specimen, and this metric can corroborate or replace empirical estimates of resolution. Other quantifiable resolution losses arise from sparse labelling, fluorescent label size, and motion blur.