This paper provides a mathematical method for airspace capacity estimation. It is motivated by the need to assess the impact of unmanned aircraft systems on low altitude airspace operations. We define capacity as a minimum of metric-specific phase transition thresholds. The definition is flexible to accommodate a wide variety of metrics defined for the airspace and hence, can be used to compare different unmanned traffic management system approaches. We provide a proof of concept using a metric based on the size of de-confliction problems. The probability of occurrence of large conflicts show phase transition as the traffic density is increased. The traffic density at phase transition i.e. the metric-specific capacity measure, increases with decreasing minimum separation tolerance. Traffic management systems which allow for a higher proximity between aircraft should therefore improve the airspace capacity. Further work must incorporate a wider range of metrics and sense and avoid algorithms for a more rigorous validation and application of our airspace capacity estimation method.