We use HST/ACS observations of the spiral galaxy M51 in F435W, F555W and F814W to select a large sample of star clusters with accurate effective radius measurements in an area covering the complete disc of M51. We present the dataset and study the radius distribution and relations between radius, colour, arm/interarm region, galactocentric distance, mass and age. We select a sample of 7698 (F435W), 6846 (F555W) and 5024 (F814W) slightly resolved clusters and derive their effective radii by fitting the spatial profiles with analytical models convolved with the point spread function. The radii of 1284 clusters are studied in detail. We find cluster radii between 0.5 and ~10 pc, and one exceptionally large cluster candidate with a radius of 21.6 pc. The median radius is 2.1 pc. We find 70 clusters in our sample which have colours consistent with being old GC candidates and we find 6 new faint fuzzy clusters in, or projected onto, the disc of M51. The radius distribution can not be fitted with a power law, but a log-normal distribution provides a reasonable fit to the data. This indicates that shortly after the formation of the clusters from a fractal gas, their radii have changed in a non-uniform way. We find an increase in radius with colour as well as a higher fraction of redder clusters in the interarm regions, suggesting that clusters in spiral arms are more compact. We find a correlation between radius and galactocentric distance which is considerably weaker than the observed correlation for old Milky Way GCs. We find weak relations between cluster luminosity and radius, but we do not observe a correlation between cluster mass and radius.
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