1. Savanna ecosystems – defined by the coexistence of trees and grasses – cover more than one‐fifth the world’s land surface and harbour most of the world’s rangelands, livestock and large mammal diversity. Savanna trees can have a variety of effects on grasses, with consequences for the wild and domestic herbivores that depend on them.

2. Studies of these effects have focused on two different spatial scales. At the scale of individual trees, many studies have shown net positive effects of trees on sub‐canopy grass nutrient concentrations and biomass. At the landscape scale, other studies have shown negative effects of high tree densities on grass productivity. These disparate results have led to different conclusions about the effects of trees on forage quality and ungulate nutrition in savannas.

3. We integrate these approaches by examining the effects of trees on grasses at both spatial scales and across a range of landscape‐scale tree densities. We quantified grass biomass, species composition and nutrient concentrations in these different contexts in an Acacia drepanolobium savanna in Laikipia, Kenya.

4. Individual trees had positive effects on grass biomass, most likely because trees enrich soil nitrogen. Grass leaf phosphorus in sub‐canopy areas, however, was depressed. The effects of individual trees could explain the effects of increasing landscape‐scale tree cover for the biomass of only two of the four dominant grass species.

5. The negative effects of trees on grass and soil phosphorus, combined with depressed grass productivity in areas of high tree cover, suggest that ungulate nutrition may be compromised in areas with many trees.

6. Synthesis. We conclude that few, isolated trees may have positive local effects on savanna grasses and forage, but in areas of high tree density the negative landscape‐scale effects of trees are likely to outweigh these positive effects. In savannas and other patchy landscapes, attempts to predict the consequences of changes in patch abundances for ecosystem services (e.g. rangeland productivity and carbon sequestration) will depend on our understanding of the extent to which local, patch‐scale dynamics do or do not predict landscape‐scale dynamics.