Summary: The question posed by the title of this study is a basic one, and it is surprising that the answer is not known. Recently, assembled trait data sets provide an opportunity to address this, but scaling these data sets to the global scale is challenging because of sampling bias. Although we currently know the growth form of tens of thousands of species, these data are not a random sample of global diversity; some clades are exhaustively characterized, while others we know little to nothing about. Starting with a data base of woodiness for 39 313 species of vascular plants (12% of taxonomically resolved species, 59% of which were woody), we estimated the status of the remaining taxonomically resolved species by randomization. To compare the results of our method to conventional wisdom, we informally surveyed a broad community of biologists. No consensus answer to the question existed, with estimates ranging from 1% to 90% (mean: 31.7%). After accounting for sampling bias, we estimated the proportion of woodiness among the world's vascular plants to be between 45% and 48%. This was much lower than a simple mean of our data set and much higher than the conventional wisdom. Synthesis. Alongside an understanding of global taxonomic diversity (i.e. number of species globally), building a functional understanding of global diversity is an important emerging research direction. This approach represents a novel way to account for sampling bias in functional trait data sets and to answer basic questions about functional diversity at a global scale.