Most futons require a set of full-size sheets, which measure about 54 inches across. However, this does not mean that sheets that are perfectly made for a bed can properly fit a futon.
Because futons fold in half, they require their own special sheets that have elastic in the band all the way around. These sheets are necessary to keep the sheets from slipping off while the futon is in its couch position. Futon sheets are also more expensive than normal bed sheets, most likely due to the differences. Futon sheets are usually purchasable anywhere that regular bed sheets and sets are sold.