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Conductivity is an important property of nano ink when considering printable electrical devices need low current loss and high frequency application. Some of the mechanical, chemical and physical characteristics that can affect the conductivity of nano ink are contact resistance, impurity, void volume, aspect ratio, particle shapes, and packing density. Increasing the packing density is one of the most important factors in increasing nano ink conductivity. A computer modeling code was developed to simulate 2 dimension packing factor (2D-PF: covered area by circle/total area of domain, %) using statistics and probability theory. The values calculated in the 2D-PF were similar to empirical 3 dimension PF (3D-PF; volume of occupied by particles/ total volume of system, %) values. The observed volume fraction of voids using spherical balls could be applied to printable ink. The highest 2D-PF calculated by 2D particles model simulation was 60% (binary) when the ratio of large to small particles size was 6. The fraction of void volume was observed empirically for binary packing systems using various ball sizes. The highest 3D-PF observed was 75.5% when the ratio of large particle to small particle was 10and the volume fraction of small particles was 0.3. The 2D-PF results calculated using 2D computer simulation agreed with the results found in actual experiments. This work studies the relationship of how packing-density and surface-contact affects conductivity of patterns using printable nano inks.