Fire ants vary in size from 2mm to 6mm; carpenter ants vary from 7.6mm to 25.4mm, according to Wikipedia. So the largest fire ant is about 1/4 (25%) of the largest carpenter ant; and the smallest fire ant is about 1/4 the size of the smallest carpenter ant. The average fire ant is about 4mm long, while the average carpenter ant is about 16.5mm long. From these figures then it would take about 4 fire ants to make up the length of one carpenter ant, on average. The shortest carpenter ant is slightly longer than the longest fire ant. The longest carpenter ant is more than 12 times the length of the shortest fire ant. In a colony of either species of ant it appears that the shortest are about a third the length of the longest, and size may be the leading factor in their social roles, so comparing ant sizes perhaps ants performing the same social roles should be compared. The most probable answer is 1 carpenter ant is 4 times the length of a fire ant in a corresponding role.