Power can be applied in different domains (e.g., politics, work, romantic relationships, family etc.), however, we do not always reflect on which domains we have power in and how important power in these domains is. A dominant idea is that men have more power than women. This notion may be biased because the concept of power is associated with public life. We introduce the concept of preference-weighted power (PWP), a measure of power that includes different domains in life, weighted by the domains' subjective importance. Two studies investigated power from this perspective. In Study 1, participants generated words related to power, which were quantified/categorized by latent semantic analysis to develop a semantic measure of the power construct. In Study 2, we computed a PWP index by weighting the participants' self-rated power in different power domains with the importance of having power in that domain. Together the studies suggest that men have more perceived power in the public domain, however, this domain has a lower preference weighting than the private domain where women have more power than men. Finally, when preferences for power in different domains were considered, no gender differences were observed. These results emphasize gender difference in different domains and may change how we perceive men's and women's power in our society.