At what age do babies outgrow their swings?

Depending : On size of your baby. Babies that are smaller can use it longer while babies that are much much bigger will only enjoy it for a very short period of time. Personally I do not recommend buying one.Some babies do not like it.You can calm your baby in other ways.

By 4 months, or : when their feet can touch the floor. Swings & walkers ABduct the hips, an abnormal position for learning to creep, crawl, cruise & walk. Start "floor time " play with baby in prone position as early as possible, ditch the swing at 2-3 months & don't waste money on a walker.