Despite the vast diversity of sizes and shapes of living organisms, life's organization across scales exhibits remarkable commonalities, most notably through the approximate validity of Kleiber's law, the power law scaling of metabolic rates with the mass of an organism. Here, we present a derivation of Kleiber's law that is independent of the specificity of the myriads of organism species. Specifically, we account for the distinct geometries of trees and mammals as well as deviations from the pure power law behavior of Kleiber's law, and predict the possibility of life forms with geometries intermediate between trees and mammals. We also make several predictions in excellent accord with empirical data. Our theory relates the separate evolutionary histories of plants and animals through the fundamental physics underlying their distinct overall forms and physiologies.