Measuring viscosity is important for the quality assurance of liquid products, as well as for monitoring the viscosity of clinical fluids as a potential hemodynamic biomarker. However, conventional viscometers and their microfluidic counterparts typically rely on bulky and expensive equipment, and lack the ability for rapid and field-deployable viscosity analysis. To address these challenges, we describe 3D-printed capillary circuits (3D-CCs) for equipment- and calibration-free viscosity measurement of Newtonian and non-Newtonian fluids. A syringe, modified with an air chamber serving as a pressure buffer, generates and maintains a set pressure to drive the pressure-driven flows of test fluids through the 3D-CCs. The graduated fluidic chambers of the 3D-CCs serve as a flow meter, enabling simple measurement of the flow rates of the test fluids flowing through the 3D-CCs, which is readable with the naked eye. The viscosities of the test fluids can be simply calculated from the measured flow rates under a set pressure condition without the need for peripheral equipment and calibration. We demonstrate the multiplexing capability of the 3D-CC platform by simultaneously measuring different Newtonian-fluid samples. Further, we demonstrate that the shear-rate dependence of the viscosity of a non-Newtonian fluid can be analyzed simultaneously under various shear-rate conditions with the 3D-CC platform.