My grandmother was a weaver, she made all her hand woven placemats at least 18 inches wide and 12 inches tall. She was old school and believed that all the utensils, dishes, glass ware had to be on the placemat. She also used rigid mats in the middle of placemats, to protect her oak table from hot plates (plates are always heated for a hot meal in our family). A bread and butter plate could be off the placemat.
So the other variable is the size of dinner ware and the number of utensils and glasses that need to be accommodated. Smaller plates with just a knife, fork and spoon, plus one glass need less room that a more formal place setting.
I have a very narrow dining room table, to fit my narrow dining room. I have used matching long runners across the table so each end becomes a place mat for that seat. Or I use placemats, but I do not have room for runners and placemat together.
Mostly I use vintage embroidered and hand made lace table cloths. I will put a place mat on top if I am dining alone or if I have guests and we are eating something potentially messy like spaghetti.