Generally,the statistical methods are defined as appropriate techniques to study the processes trends. In current research, the Fe3O4 superparamagnetic nanoparticles were synthesized by coprecipitation method. In order toi nvestigate the size properties of synthesized particles, the experimental design was done using central composite method(CCD) of response surface methodology(RSM) while the tem- perature, pH, and cation ratio of reaction were selected as influential factors.After particles synthesis based on designed runs, the different responses such as hydrodynamic size of particles(both freeze dried and air dried),size distribution, crystallite size,magnetic size,and zeta potential were evaluated by different techniques i.e.dynamic light scattering(DLS), X-ray diffraction(XRD), and vibrating sample magnetometer(VSM). Based on the seresults, the quadratic polynomial model was fitted for eachre- sponse that could predict the response amounts. In following, the study of factors effects was carried out that showed the temperature, pH, and the irinteraction shad higher effectiveness.Finally, by optimizing, it was clear that the minimum amounts of particle size (10.15nm) and size distribution(13.01nm) were reached in the minimum temperature(70 °C) and cation ratio (0.5) amounts and maximum pH amount (10.5). Moreover, the characterizations showed the particles size was about 10nm while the amounts of Ms, Hc, and Mr were equal to 60(emu/g), 0.2(Oe) and 0.22(emu/g), respectively.

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