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Forest canopy structural complexity (CSC), an emergent ecosystem property, plays a critical role in controlling ecosystem productivity, resource acquisition and resource use‐efficiency; yet is poorly characterized across broad geographic scales and is difficult to upscale from the plot to the landscape.Here, we show that the relationship between canopy height and CSC can be explained using power laws by analysing lidar‐derived CSC data from 17 temperate forest sites spanning over 17 degrees of latitude. Across three plant functional types (deciduous broadleaf, evergreen needleleaf and mixed forests), CSC increases as an approximate power law of forest height. In evergreen needleleaf forests, increases in canopy height do not result in increases in complexity to the same magnitude as in other forest types.We attribute differences in the slope of height:complexity relationships among forest types to: (a) the limited diversity of crown architectures among evergreen conifer trees relative to broadleaf species; (b) differences in how vertical forest layering develops with height; and (c) competitive exclusion by needleleaf species. We show support for these potential mechanisms with an analysis of 4,324 individual trees from across 18 National Ecological Observatory Network sites showing that crown geometry‐to‐tree height relationships differ consistently between broadleaf and needleleaf species.Power law relationships between forest height and CSC have broad implications for modelling, scaling and mapping forest structural attributes. Our results suggest that forest research and management should consider the nonlinearity in scaling between forest height and CSC and that the nature of these relationships may differ by forest type. A free Plain Language Summary can be found within the Supporting Information of this article. [ABSTRACT FROM AUTHOR]