This study proposes a new metric called canopy geometric volume G, which is derived from small-footprint lidar data, for estimating individual-tree basal area and stem volume. Based on the plant allometry relationship, we found that basal area B is exponentially related to G (B = β1G3/4, where β1 is a constant) and stem volume V is proportional to G (V = β2G, where β2 is a constant). The models based on these relationships were compared with a number of models based on tree height and/or crown diameter. The models were tested over individual trees in a deciduous oak woodland in California in the case that individual tree crowns are either correctly or incorrectly segmented. When trees are incorrectly segmented, the theoretical model B = β1G3/4 has the best performance (adjusted R2, R2 a = 0.78) and the model V = β2G has the second to the best performance (R2 a = 0.78). When trees are correctly segmented, the theoretical models are among the top three models for estimating basal area (R2 a = 0.77) and stem volume (R2 a = 0.79). Overall, these theoretical models are the best when considering a number of factors such as the performance, the model parsimony, and the sensitivity to errors in tree crown segmentation. Further research is needed to test these models over sites with multiple species.