The transport properties of hydrogels largely affect their performance in biomedical applications ranging from cell culture scaffolds to drug delivery systems. Solutes can move through the polymer mesh as a result of concentration gradients in the interstitial fluid or pressure gradients that move the fluid and solutes simultaneously. The relationship between the two modalities of transport in hydrogels can provide insight for the design of materials that can function effectively in the dynamic conditions experienced in vitro and in vivo, yet this correlation has not been previously elucidated. Here, fluorescence recovery after photobleaching (FRAP) is used to measure the diffusivity of dextran molecules of different size within polyethylene glycol hydrogels. Spherical indentation analyzed in a poroelastic framework is used to measure the permeability to fluid flow of the same hydrogels. It is found that while the diffusivity varies with exp(ξ -2), where ξ is the mesh size of the hydrogels, it also varies with exp(k -1), where k is the intrinsic permeability. For the same hydrogel structure, diffusive transport is affected by the solute size, while convective transport is unaffected. As spherical indentation is a reliable, quick and non-destructive testing method for hydrated soft materials, the relationship provides the means to faster assessment of the transport properties of hydrogels and, ultimately, of their effective use in biomedical applications.