Extending previous work on the predictions for the production of supersymmetric (SUSY) particles at the LHC, we present the fully differential calculation of the next-to-leading order (NLO) SUSY-QCD corrections to the production of squark and squark–antisquark pairs of the first two generations. The NLO cross sections are combined with the subsequent decay of the final state (anti)squarks into the lightest neutralino and (anti)quark at NLO SUSY-QCD. No assumptions on the squark masses are made, and the various subchannels are taken into account independently. In order to obtain realistic predictions for differential distributions the fixed-order calculations have to be combined with parton showers. Making use of the Powheg method we have implemented our results in the Powheg-Box framework and interfaced the NLO calculation with the parton shower Monte Carlo programs Pythia6 and Herwig++. The code is publicly available and can be downloaded from the Powheg-Box webpage. The impact of the NLO corrections on the differential distributions is studied and parton shower effects are investigated for different benchmark scenarios.