Above-ground tropical tree biomass and carbon storage estimates commonly ignore tree height. We estimate the effect of incorporating height (H) on forest biomass estimates using 37 625 concomitant H and diameter measurements (n = 327 plots) and 1816 harvested trees (n = 21 plots) tropics-wide to answer the following questions: 1. For trees of known biomass (from destructive harvests) which H-model form and geographic scale (plot, region, and continent) most reduces biomass estimate uncertainty? 2. How much does including H relationship estimates derived in (1) reduce uncertainty in biomass estimates across 327 plots spanning four continents? 3. What effect does the inclusion of H in biomass estimates have on plot- and continental-scale forest biomass estimates? The mean relative error in biomass estimates of the destructively harvested trees was half (mean 0.06) when including H, compared to excluding H (mean 0.13). The power- and Weibull-H asymptotic model provided the greatest reduction in uncertainty, with the regional Weibull-H model preferred because it reduces uncertainty in smaller-diameter classes that contain the bulk of biomass per hectare in most forests. Propagating the relationships from destructively harvested tree biomass to each of the 327 plots from across the tropics shows errors are reduced from 41.8 Mg ha-1 (range 6.6 to 112.4) to 8.0 Mg ha-1 (-2.5 to 23.0) when including $H$. For all plots, above-ground live biomass was 52.2±17.3 Mg ha-1 lower when including H estimates (13%), with the greatest reductions in estimated biomass in Brazilian Shield forests and relatively no change in the Guyana Shield, central Africa and southeast Asia. We show fundamentally different stand structure across the four forested tropical continents, which affects biomass reductions due to $H$. African forests store a greater portion of total biomass in large-diameter trees and trees are on average larger in diameter. This contrasts to forests on all other continents where smaller-diameter trees contain the greatest fractions of total biomass. After accounting for variation in $H$, total biomass per hectare is greatest in Australia, the Guyana Shield, and Asia and lowest in W. Africa, W. Amazonia, and the Brazilian Shield (descending order). Thus, if closed canopy tropical forests span 1668 million km2 and store 285 Pg C, then the overestimate is 35 Pg C if H is ignored, and the sampled plots are an unbiased statistical representation of all tropical forest in terms of biomass and height factors. Our results show that tree $H$ is an important allometric factor that needs to be included in future forest biomass estimates to reduce error in estimates of pantropical carbon stocks and emissions due to deforestation. ; Additional co-authors: L. E. O. C. Aragão, A. Araujo Murakami, E. J. M. M. Arets, L. Arroyo, G. A. Aymard C., T. R. Baker, O. S. Bánki, N. J. Berry, N. Cardozo, J. Chave, J. A. Comiskey, E. A. Dávila, A. de Oliveira, A. DiFiore, G. Djagbletey, T. F. Domingues, T. L. Erwin, P. M. Fearnside, M. B. França, M.A. Freitas, N. Higuchi, E. Honorio C., Y. Iida, E. Jiménez, A. R. Kassim, T. J. Killeen, W. F. Laurance, J. C. Lovett, Y. Malhi, B. S. Marimon, B. H. Marimon-Junior, E. Lenza, A. R. Marshall, C. Mendoza, D. J. Metcalfe, E. T. A. Mitchard, B. W. Nelson, R. Nilus, E. M. Nogueira, A. Parada, K. S.-H. Peh, A. Pena Cruz, M. C. Peñuela, N. C. A. Pitman, A. Prieto, C.A. Quesada, F. Ramírez, H. Ramírez-Angulo, J. M. Reitsma, A. Rudas, G. Saiz, R. P. Salomão, M. Schwarz, N. Silva, J. E. Silva-Espejo, M. Silveira, B. Sonké, J. Stropp, H. E. Taedoumg, S. Tan, H. ter Steege, J. Terborgh, M. Torello-Raventos, G. M. F. van der Heijden, R. Vásquez, E. Vilanova, V. Vos, S. Wilcock, H. Woell, and O. L. Phillips