- We present results from strong lens modelling of 10 000 Sloan Digital Sky Survey (SDSS) clusters, to establish the universal distribution of Einstein radii. Detailed lensing analyses have shown that the inner mass distribution of clusters can be accurately modelled by assuming light traces mass, successfully uncovering large numbers of multiple images. Approximate critical curves and the effective Einstein radius of each cluster can therefore be readily calculated, from the distribution of member galaxies and scaled by their luminosities. We use a subsample of 10 well-studied clusters covered by both SDSS and Hubble Space Telescope (HST) to calibrate and test this method, and show that an accurate determination of the Einstein radius and mass can be achieved by this approach ‘blindly’, in an automated way, and without requiring multiple images as input. We present the results of the first 10 000 clusters analysed in the range 0.1 < z < 0.55 and compare them to theoretical expectations. We find that for this all-sky representative sample the Einstein radius distribution is lognormal in shape, with , , and with higher abundance of large θe clusters than predicted by Λ cold dark matter. We visually inspect each of the clusters with (zs= 2) and find that ∼20 per cent are boosted by various projection effects detailed here, remaining with ∼40 real giant-lens candidates, with a maximum of (zs= 2) for the most massive candidate, in agreement with semi-analytic calculations. The results of this work should be verified further when an extended calibration sample is available.