Many animal species are detected primarily by sound. Although songs, calls and other sounds are often used for population assessment, as in bird point counts and hydrophone surveys of cetaceans, there are few rigorous methods for estimating population density from acoustic data. 2. The problem has several parts - distinguishing individuals, adjusting for individuals that are missed, and adjusting for the area sampled. Spatially explicit capture-recapture (SECR) is a statistical methodology that addresses jointly the second and third parts of the problem. We have extended SECR to use uncalibrated information from acoustic signals on the distance to each source. 3. We applied this extension of SECR to data from an acoustic survey of ovenbird Seiurus aurocapilla density in an eastern US deciduous forest with multiple four-microphone arrays. We modelled average power from spectrograms of ovenbird songs measured within a window of 0??7 s duration and frequencies between 4200 and 5200 Hz. 4. The resulting estimates of the density of singing males (0??19 ha ^-1 SE 0??03 ha^-1) were consistent with estimates of the adult male population density from mist-netting (0??36 ha^-1 SE 0??12 ha^-1). The fitted model predicts sound attenuation of 0??11 dB m^-1 (SE 0??01 dB m^-1) in excess of losses from spherical spreading. 5.Synthesis and applications. Our method for estimating animal population density from acoustic signals fills a gap in the census methods available for visually cryptic but vocal taxa, including many species of bird and cetacean. The necessary equipment is simple and readily available; as few as two microphones may provide adequate estimates, given spatial replication. The method requires that individuals detected at the same place are acoustically distinguishable and all individuals vocalize during the recording interval, or that the per capita rate of vocalization is known. We believe these requirements can be met, with suitable field methods, for a significant number of songbird species. ?? 2009 British Ecological Society.