► Participants included 393 university students. ► A negative binomial regression strategy was used to analyse count data. ► Openness was associated with spending time and having friends on Facebook. ► Loneliness was associated with having Facebook friends. This study examined the relationship between three of the “Big Five” traits (neuroticism, extraversion, and openness), self-esteem, loneliness and narcissism, and Facebook use. Participants were 393 first year undergraduate psychology students from a medium-sized Australian university who completed an online questionnaire. Negative binomial regression models showed that students with higher openness levels reported spending more time on Facebook and having more friends on Facebook. Interestingly, students with higher levels of loneliness reported having more Facebook friends. Extraversion, neuroticism, self-esteem and narcissism did not have significant associations with Facebook use. It was concluded that students who are high in openness use Facebook to connect with others in order to discuss a wide range of interests, whereas students who are high in loneliness use the site to compensate for their lack of offline relationships.