A peanut cultivar designated UFT113 is disclosed. The invention relates to the seeds, the plants, and the plant parts of peanut cultivar UFT113, and to methods for producing a peanut plant by crossing peanut cultivar UFT113 with itself or with another peanut variety. The invention also relates to methods for producing a peanut plant containing in its genetic material one or more transgenes and to the transgenic peanut plants and plant parts produced by those methods. This invention also relates to peanut cultivars, or breeding cultivars, and plant parts derived from peanut cultivar UFT113, to methods for producing other peanut cultivars, lines or plant parts derived from peanut cultivar UFT113, and to the peanut plants, varieties, and their parts derived from use of those methods. The invention further relates to hybrid peanut seeds, plants, and plant parts produced by crossing cultivar UFT113 with another peanut cultivar.