Car traffic in urban systems has been studied intensely in past decades but its analysis is often limited to empirical observations and agent-based modelling, and despite the importance and urgency of the problem we have a poor theoretical understanding of the parameters controlling urban car use and congestion. Here, we combine economical and transport ingredients into a statistical physics approach and propose a parsimonious model that predicts the share of car drivers, the $CO_2$ emitted by cars and the average commuting time. We confirm these analytical predictions on 25 major urban areas in the world, and our results suggest that urban density is not the relevant variable controlling car-related quantities but rather are the city's area size and the density of public transport. Mitigating the traffic (and its effect such as $CO_2$ emissions) can then be obtained by reducing the urbanized area size or, more realistically, by improving either the public transport density or its access. In general, increasing the population at fixed area would increase the emission of $CO_2$ in sharp contrast with the commonly accepted paradigm that increasing the density leads to a reduction of car traffic.