The theory of the equation of state of a surface monolayer formulated earlier and based on an analysis of the exclusion factor was extended to the whole density range by implementing approximations of higher orders. The equations were derived to satisfy the requirement of maximum simplicity and contained a single adjustment parameter found by numerically simulating a fluid of hard disks. The accuracy of the equation of state was raised to 0.46% over the whole density range. The equations obtained are compared with the most popular modern equations of state.