A low-cost and simple setup to measure the densities of liquids is introduced herein. The results and reliability of this setup were evaluated for pure liquids, water-ethanol binary mixtures, and aqueous NaCl solutions. The constructed densitometer provided density values with acceptable relative errors (less than ±3.0%), which were compared to estimates of density from the literature. The favorable agreement is surprising for such a simple and low-cost setup. The facile design lends itself to use in diverse teaching environments to reinforce the ubiquitous concept of density at the secondary-school level and for undergraduate physical-chemistry teaching laboratories.