Printed batteries are an emerging solution for integrated energy storage using low-cost, high accuracy fabrication techniques. While several printed batteries have been previously shown, few have designed a battery that can be incorporated into an integrated device. Specifically, a fully printed battery with a small active electrode area (<1 cm(2)) achieving high areal capacities (>10 mAh cm(-2)) at high current densities (1-10 mA cm(-2)) has not been demonstrated, which represents the minimum form-factor and performance requirements for many low-power device applications. This work addresses these challenges by investigating the scaling limits of a fully printed Zn-Ag2O battery and determining the electrochemical limitations for a mm(2)-scale battery. Processed entirely in air, Zn-Ag2O batteries are well suited for integration in typical semiconductor packaging flows compared to lithium-based chemistries. Printed cells with electrodes as small as 1 mm(2) maintain steady operating voltages above (>1.4 V) at high current densities (1-12 mA cm(-2)) and achieve the highest reported areal capacity for a fully printed battery at 11 mAh cm(-2). The findings represent the first demonstration of a small, packaged, fully printed Zn-Ag2O battery with high areal capacities at high current densities, a crucial step toward realizing chip-scale energy storage for integrated electronic systems.