With a goal toward deriving the physical conditions in external galaxies, we present a survey of the formaldehyde emission in a sample of starburst systems. By extending a technique used to derive the spatial density in star formation regions in our own Galaxy, we show how the relative intensity of the 110-111 and 211-212 K-doublet transitions of H2CO can provide an accurate densitometer for the active star formation environments found in starburst galaxies. Relying on an assumed kinetic temperature and cospatial emission and absorption from both H2CO transitions, our technique is applied to a sample of 19 infrared-bright galaxies which exhibit various forms of starburst activity. In the five galaxies of our sample where both H2CO transitions were detected, we have derived spatial densities. We also use H2CO to estimate the dense gas mass in our starburst galaxy sample, finding similar mass estimates for the dense gas-forming stars in these objects as derived using other dense gas tracers. A related trend can be seen when one compares LIR to our derived n(H2) for the five galaxies within which we have derived spatial densities. Even though our number statistics are small, there appears to be a trend toward higher spatial density for galaxies with higher infrared luminosity. This is likely another representation of the LIR-Mdense correlation.