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The species – area relationship (SAR) is a common pattern in which diversity increases with the area sampled, but ecosystems are three‐dimensional (3D) and diversity – volume relationships (DVRs) may exist in ecosystems that vary substantially in their vegetation volume. We tested whether forest vegetation volume, as a 3D extension of area in SARs, was a significant predictor of taxonomic (species) and structural (arrangement) diversity in five groups of organisms across the National Ecological Observatory Network (NEON). Vegetation volume and four structural arrangement metrics within the area of NEON plots were measured using NEON's discrete return lidar. Species richness was measured as the number of species within the respective NEON plot sampling area for understory plants, trees, breeding land birds, small mammals, and ground beetles. We found that volume negatively predicted understory plants and positively predicted tree and beetle species richness across the USA forest macrosystem, but not bird and small mammal species richness. Furthermore, volume was a significant predictor of several metrics that describe the internal and external heterogeneity of vegetation in forests (structural arrangement) within the ecosystem across the USA forest macrosystem. There were several significant within site‐level relationships, but not at all sites, between volume and species richness or structural arrangement in organism groups. Our study indicates that previous work that has focused on a 2D conceptualization of habitat can be expanded to 3D habitat space, but that the strength and the positive or negative direction of DVRs may vary taxonomically or geographically.