To predict the ecological consequences of biodiversity loss, researchers have spent much time and effort quantifying how biological variation affects the magnitude and stability of ecological processes that underlie the functioning of ecosystems. Here we add to this work by looking at how biodiversity jointly impacts two aspects of ecosystem functioning at once: (1) the production of biomass at any single point in time (biomass/area or biomass/volume), and (2) the stability of biomass production through time (the CV of changes in total community biomass through time). While it is often assumed that biodiversity simultaneously enhances both of these aspects of ecosystem functioning, the joint distribution of data describing how species richness regulates productivity and stability has yet to be quantified. Furthermore, analyses have yet to examine how diversity effects on production covary with diversity effects on stability. To overcome these two gaps, we reanalyzed the data from 34 experiments that have manipulated the richness of terrestrial plants or aquatic algae and measured how this aspect of biodiversity affects community biomass at multiple time points. Our reanalysis confirms that biodiversity does indeed simultaneously enhance both the production and stability of biomass in experimental systems, and this is broadly true for terrestrial and aquatic primary producers. However, the strength of diversity effects on biomass production is independent of diversity effects on temporal stability. The independence of effect sizes leads to two important conclusions. First, while it may be generally true that biodiversity enhances both productivity and stability, it is also true that the highest levels of productivity in a diverse community are not associated with the highest levels of stability. Thus, on average, diversity does not maximize the various aspects of ecosystem functioning we might wish to achieve in conservation and management. Second, knowing how biodiversity affects productivity gives no information about how diversity affects stability (or vice versa). Therefore, to predict the ecological changes that occur in ecosystems after extinction, we will need to develop separate mechanistic models for each independent aspect of ecosystem functioning.