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Peer-to-peer (P2P) carpooling has become an effective way to utilize the idle car capacity and ease traffic congestion. However, the interactive relationship between carpooling and traffic congestion has not been fully quantified. To make up for this gap, this paper constructs a side-constrained P2P carpooling stochastic user equilibrium model to disclose the effects of carpooling on traffic congestion. Next, the proposed model was transformed into a linear constrained minimization problem, and the problem was proved to have a unique solution. The case study shows that the travellers prefer carpooling at a high fuel price and a low inconvenient cost.