Tropical forests are global centres of biodiversity and carbon storage. Many tropical countries aspire to protect forest to fulfil biodiversity and climate mitigation policy targets, but the conservation strategies needed to achieve these two functions depend critically on the tropical forest tree diversity-carbon storage relationship. Assessing this relationship is challenging due to the scarcity of inventories where carbon stocks in aboveground biomass and species identifications have been simultaneously and robustly quantified. Here, we compile a unique pan-tropical dataset of 360 plots located in structurally intact old-growth closed-canopy forest, surveyed using standardised methods, allowing a multi-scale evaluation of diversity-carbon relationships in tropical forests. Diversity-carbon relationships among all plots at 1 ha scale across the tropics are absent, and within continents are either weak (Asia) or absent (Amazonia, Africa). A weak positive relationship is detectable within 1 ha plots, indicating that diversity effects in tropical forests may be scale dependent. The absence of clear diversity-carbon relationships at scales relevant to conservation planning means that carbon-centred conservation strategies will inevitably miss many high diversity ecosystems. As tropical forests can have any combination of tree diversity and carbon stocks both require explicit consideration when optimising policies to manage tropical carbon and biodiversity.