The nervous system scales with animal size, maintaining function while minimizing wire. In contrast to most animal organs, which scale through the proliferation of dividing cells of similar size, brains expand by modulating the size of non-dividing neuronal cells to innervate space during development. As a result, there is notable diversity in neuronal size and structure within individual brains and between different species. This diversity raises an important question: how do neurons maintain computational function across diverse sizes while minimizing wiring costs? Two theoretical results have been proposed to address these problems. On one hand, the dendritic constancy principle posits that invariant synaptic density ensures stable neuronal firing rates across varying dendritic shapes, preserving functional stability. Meanwhile, an influential morphological scaling law derived from optimal wiring principles posits a 2/3 power-law relationship between dendritic length, spanning volume, and synapse number. Testing these principles has been challenging due to a lack of ultrastructural data on dendritic trees and their connectivity. To address this, we analyzed thousands of reconstructed single-cell morphologies from EM-derived connectomes across Drosophila, zebrafish, mouse, and human to explore how neuronal structure scales with function. In line with the dendritic constancy principle, we found that synapse density remains remarkably invariant, averaging one synapse per micrometer across species. Analysis of genetically modified Drosophila shows that precise partner location and synaptic activity are crucial to achieve this density during development. We also confirm the quantitative match between real morphological data and the 2/3 power-law scaling relationship. To directly link synaptic density invariance and wiring optimization scaling, we performed a sensitivity analysis using this law to show that density invariance is linked to dendritic structure arising from wiring minimization constraints. Our findings suggest that the convergence in synaptic density serves as a functional backbone for computational stability, while connecting principles of resource optimization and functional stability across evolutionary and developmental scales.