Stray dogs and cats contribute to serious health problems in human societies around the world. Before any necessary interventions to control the stray dogs and cats, an accurate estimate of their populations should be attained. Yet, there is a very limited number of methods for an estimation. Some of them depend on the identification of marked or counted animals. However, problems arise when it is not possible to identify a previously captured animal. In this paper, we used a different approach to estimate the lower bound for the total number of dogs and cats in consecutively visited settlements that might be useful for future studies internationally. It was estimated that there were 17,839 (95% CI: 14,862-20,816) stray dogs and 10,191 (95% CI: 8439-11,942) stray cats in Ankara, Turkey. The results highlight the need for a science-based policy to control and manage the stray dog and cat populations in Ankara.