Fracture characterization protocols that reduce sampling bias are likely to yield higher quality input for exploration and development decisions when dealing with naturally fractured reservoirs. A new set of estimators for fracture density, intensity, and mean trace length corrects for sampling biases and provides a useful integrated description for bulk aspects of a fracture network. These estimators are based on counts of intersections between fracture traces and circular scan lines and of trace terminations in circular windows. Application to synthetic fracture patterns with known parameters validates the use of the new estimators, which are then applied to natural fault trace maps from seismic volumes and joint trace maps from rock pavements. The new estimators are distribution independent and eliminate the effects of orientation, censoring, and length biases, which limit the effectiveness of other sampling techniques. Estimator accuracy improves as sample size increases, particularly for larger circles that exceed a fracture-defined block size. Estimator accuracy for mean trace length improves when the sample exceeds threshold count values for fracture terminations based on guidance from the analysis of similar synthetic patterns. These new estimators also provide both inputs and independent checks of predictions for fracture-generator programs used to model fracture populations in a rock volume.