The distance likely depends on the species of hornet and perhaps on the insect's size and habitat. I’ve found several results for wasps, but not specifically for hornets, which are a type of wasp. The foraging distance is in the range of hundreds of metres, but the exact distance discovered in experiments varies.
In New Zealand, researchers set up poisonous bait stations for invasive Vespula vulgaris wasps. They found dead wasps at stations located up to 450 metres from the nest but not at those located 800 metres from the nest. A government of New Zealand document about four species of invasive wasps (including Vespula vulgaris) says that they forage mainly within 200 metres from the nest. The University of Kentucky says that yellow jacket wasps forage several hundred yards from the nest. This is roughly the same as the previous measurements, since a yard is just a little under a metre in length.