Vardaman's age is never given in the novel. He is younger than Dewey Dell, who is seventeen. Most readers seem to think of Vardaman as being between twelve and fourteen, but other readers choose to view him as a much younger boy of six or seven. There is evidence to support both views.
In Addie's statement that she "gave Anse Dewey Dell to negate Jewel. Then I gave him Vardaman to replace the child I robbed him of," the implication is that Vardaman's birth followed soon after Dewey Dell's. Thus, if Dewey Dell is seventeen, Vardaman would be only a couple of years younger. Furthermore, when someone is needed to go after Dr. Peabody's runaway team, it seems more logical for them to send a fourteen-year-old than it would be to send a seven-year-old. Finally, there are suggestions that Addie is about fifty-three at her death. If Vardaman is only seven, that would mean she gave birth at age forty-six or forty-seven, which is not impossible but is highly improbable.
In support of Vardaman's being younger, Faulkner himself in Faulkner at the University refers to Vardaman as a "child." Several images suggest that he is a very young person. For example, the fish he caught is almost as big as he is, and there are few fish in Mississippi ponds almost as large as a fourteen-year-old boy. Furthermore, when he is standing at Tull's door, he cannot be seen by the adult man, suggesting that he is rather small.
In general, Vardaman's actions, such as boring a hole in his mother's coffin, suggest that he is either a young boy incapable of understanding death or that he is a mentally slow fourteen-year-old.