Are lockdown policies effective at inducing physical distancing to counter the spread of COVID-19? Can less restrictive measures that rely on voluntary community action achieve a similar effect? Using data from 40 million mobile devices, we find that a lockdown increases the percentage of people who stay at home by 8% across US counties. Grouping states with similar outbreak trajectories together and using an instrumental variables approach, we show that time spent at home can increase by as much as 39%. Moreover, we show that individuals engage in limited physical distancing even in the absence of such policies, once the virus takes hold in their area. Our analysis suggests that non-causal estimates of lockdown policies’ effects can yield biased results. We show that counties where people have less distrust in science, are more highly educated, or have higher incomes see a substantially higher uptake of voluntary physical distancing. This suggests that the targeted promotion of distancing among less responsive groups may be as effective as across-the-board lockdowns, while also being less damaging to the economy.