In cold bulk forming processes, a constant shear friction model is widely used to apply friction. However, it is not easy to predict the shear friction factor since frictional behavior is highly nonlinear and is dependent upon a number of processing variables, such as the hardness of the material, lubricity, sliding velocity, surface contact conditions, and the environment, etc. This paper presents a dimensionless equation that predicts the shear friction factor at the counter punch interface mfd that was empirically determined by dimensional analysis, using the tip test results available in the literature as a function of selected process variables, such as the yield strength and initial specimen's radius of the deforming material, hardness, and surface roughness of the deforming material and the counter punch, viscosity of the lubricant, and deformation speed. To verify the determined equation, a new set of experiments were carried out for specimens made of AL7075-O. The prediction of the shear friction factor at the punch interface was also achieved by simply dividing the dimensionless equation by the x ratio defined by x = mfd/mfp, which is dependent on the hardening exponent of the deforming material based on previous studies. The predicted mfd and mfp were found to be reasonable owing to comparisons with the experimental data obtained for AL7075–O in this study. These results will be beneficial in scientifically assessing the effect of the processing parameters on the friction, individually and economically selecting the lubrication condition for cold bulk forming for practical applications.