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• A diffusion method for characterising cellular suspensions is presented. • Cell count, water exchange rates and interior/exterior diffusion/relaxation rates are obtained from fitting. • Monte Carlo simulations validate the model and demonstrate its versatility. • Results are not particularly dependent on the geometry of cells under study. • Successful applications to yeast and 3T3 and HeLa mammalian cells are shown. NMR and MRI diffusion experiments contain information describing the shape, size, abundance, and membrane permeability of cells although extracting this information can be challenging. Here we present the INDIANA (IN-cell DIffusion ANAlysis) method to simultaneously and non-invasively measure cell abundance, effective radius, permeability and intrinsic relaxation rates and diffusion coefficients within the inter- and intra-cellular populations. The method couples an experimental dataset comprising stimulated-echo diffusion measurements, varying both the gradient strength and the diffusion delay, together with software to fit a model based on the Kärger equations to robustly extract the relevant parameters. A detailed error analysis is presented by comparing the results from fitting simulated data from Monte Carlo simulations, establishing its effectiveness. We note that for parameters typical of mammalian cells the approach is particularly effective, and the shape of the underlying cells does not unduly affect the results. Finally, we demonstrate the performance of the experiment on systems of suspended yeast and mammalian cells. The extracted parameters describing cell abundance, size, permeability and relaxation are independently validated. [ABSTRACT FROM AUTHOR]