The effects of particle size and density on the mixing behaviour of binary mixtures of spheres in a vertically-shafted bladed mixer are studied by means of the discrete element method. To characterise the mixing behaviour, a particle scale mixing index is used. The results reveal that for a given volume fraction, there are optimum small-to-large size ratio and light-to-heavy density ratio that can provide the maximum mixing index. That is, the particle size and density differences can interact with each other, sometimes improving mixing. The mechanism behind this mixing improvement is confirmed by the analysis of vertical forces on particles. The improvement occurs because large-heavy particles can sink to the vessel base under their heavy weight instead of being pushed upwards by the vertical force generated due to the size-difference. Small-light particles move on top of the large particles, improving the mixing behaviour. The volume fraction of the mixing particles also affects the mixing behaviour. The effects of particle size, density and volume fraction can be quantified in detail, and an empirical predictive equation to describe these effects is established for this purpose based on the simulated results. The equation can be used to determine the particle size and density ratios that result in an identical mixing quality, generating a comprehensive picture about the size and density equivalence in relation to mixing. Such a quantitative description is promising in application in that the present mixing system with its simple geometry can be used as a standard reference mixer for quantifying the effects of particle properties.