The mass-detecting technique has been applied to design a capillary viscometer for viscosity measurements of both Newtonian and non-Newtonian fluids over a range of shear rates. Flow-rate and pressure-drop measurements are replaced with a measurement of liquid-mass variation with time. Using a precision balance, one can measure the variation of fluid mass collected in the receptacle, m(t), from which the test fluid viscosity and shear rate are mathematically calculated. The feasibility and accuracy of the mass-detecting technique have been demonstrated for water and non-Newtonian fluids by comparing results against established viscosity measurement techniques. The advantages of this design are simplicity (i.e., ease of operation and no moving parts), low cost, and the ability to measure viscosity over a relatively broad range of shear rates.