The total circumpolar abundance of Antarctic krill (Euphausia superba) is estimated using recent measurements of krill density from acoustic surveys and historical information on the overall range of krill. The biomass estimates fall between 60 and 155 million tonnes - at the low end of values that have been suggested in the past. The differences between our estimates and others can be explained by a number of factors such as: an underestimation of the range or the acoustic biomass estimates; the possibility of a large, undetected krill population; and the overestimation of the demand for krill by predators. Even if these low krill biomass estimates are correct, regional and total precautionary limits are still likely to rise as a result of new surveys because the method used to calculate precautionary limits uses a value of 11% of the estimated pre-exploitation biomass. Additionally, the current precautionary catch limits in the South Atlantic are set using a superseded acoustic target strength which has effectively underestimated the krill biomass by a factor of three, so the new survey of the South Atlantic in January 2000 may result in an effective biomass which is greater than the value used in the past. The seasonal and local consequences of large catch limits will have to be taken into account when managing an expanded krill fishery, and the appropriateness of using the existing statistical divisions as management areas will have to be considered.