Identifying and quantifying factors influencing human decision making remains an outstanding challenge, impacting the performance and predictability of social and technological systems. In many cases, system failures are traced to human factors including congestion, overload, miscommunication, and delays. Here we report results of a behavioral network science experiment, targeting decision making in a natural disaster. In a controlled laboratory setting, our results quantify several key factors influencing individual evacuation decision making in a controlled laboratory setting. The experiment includes tensions between broadcast and peer-to-peer information, and contrasts the effects of temporal urgency associated with the imminence of the disaster and the effects of limited shelter capacity for evacuees. Based on empirical measurements of the cumulative rate of evacuations as a function of the instantaneous disaster likelihood, we develop a quantitative model for decision making that captures remarkably well the main features of observed collective behavior across many different scenarios. Moreover, this model captures the sensitivity of individual- and population-level decision behaviors to external pressures, and systematic deviations from the model provide meaningful estimates of variability in the collective response. Identification of robust methods for quantifying human decisions in the face of risk has implications for policy in disasters and other threat scenarios, specifically the development and testing of robust strategies for training and control of evacuations that account for human behavior and network topologies.