Social distancing is often presented as an individual choice, done for one's own safeguard or general altruism : Individuals get blamed for not respecting it, and political leaders have called upon civic responsibility to comply with regulations. Social distancing however is first and foremost a change in social norms, and likely to involve conformity with one's own reference group. Existing models of norm changes and our new data provide here a new fine-grained picture of how social influence contributes to the compliance with distancing measures.