The density of a closed population of animals occupying stable home ranges may be estimated from detections of individuals on an array of detectors, using newly developed methods for spatially explicit capture–recapture. Likelihood-based methods provide estimates for data from multi-catch traps or from devices that record presence without restricting animal movement ("proximity" detectors such as camera traps and hair snags). As originally proposed, these methods require multiple sampling intervals. We show that equally precise and unbiased estimates may be obtained from a single sampling interval, using only the spatial pattern of detections. This considerably extends the range of possible applications, and we illustrate the potential by estimating density from simulated detections of bird vocalizations on a microphone array. Acoustic detection can be defined as occurring when received signal strength exceeds a threshold. We suggest detection models for binary acoustic data, and for continuous data comprising measurements of all signals above the threshold. While binary data are often sufficient for density estimation, modeling signal strength improves precision when the microphone array is small.