Data donations, where individuals are encouraged to donate their personal information, have the potential to advance medical research and help limit the spread of pandemics, among other benefits. The decision to donate data is fundamentally a privacy decision. In this research, we build on the privacy calculus, a model describing privacy risks and benefits, and examine the impact of privacy concerns on data donation decisions, highlighting the role of societal benefits in privacy decisions. Based on two randomized experiments using the general context of data donation for medical research (experiment 1) and the specific context of data donation for COVID-19 research (experiment 2), we find that individuals who are highly concerned about privacy tend to donate less data (experiments 1 and 2). This effect holds under a variety of conditions and is consistent with prevailing research. However, this effect is contingent on the privacy calculus. When implicit or explicit societal benefits are perceived, particularly in the absence of privacy controls, the association between privacy concerns and data donation decisions is less salient, highlighting the significant role that societal benefits have in privacy decisions. We discuss the theoretical, practical, social, and ethical implications of these findings.