A mantle is a covering, like a robe. But a mantel is a ledge over a fireplace. If Little Red Riding Hood tosses her cloak on the shelf above her fireplace, she has a mantle on the mantel.

Mantle is a word that covers lots of meanings. The word can refer to a covering, like ivy on a building, or to the layer of the Earth’s interior between the core and the crust. A mantle, in the sense of a type of cloak, was worn by royalty to show authority. Mantle can also refer figuratively to power or authority. In this sense, someone could take the mantle of the student council or pass the mantle to another person. Less frequently, mantle is used as a verb meaning "to cover," as in "snow mantled the trees."

Here are some examples that show mantle’s range of meanings:

According to legend, Athena sometimes cut pieces off her mantle and draped them over statues in her temples, or over her chosen heroes, to shield them. (Blood of Olympus)
Earth’s mantle was riddled with illegal tunnels, and it was impossible to police them all. (Artemis Fowl)
He returned to Mississippi in 1963 after the assassination of his younger brother, Medgar, to take up the mantle of leading the state NAACP. (Washington Times)

A mantel, on the other hand, goes over the fireplace. Although mantle has been an alternate spelling for mantel in American English, let your fireplace ledge have its glory and spell it with an el. Unlike mantle, which has many meanings, the word mantel refers only to that shelf above the fire.

Here are some mantels in the wild:

The design team did change the fireplace from a faux Victorian design to a simple modern rendition with a white plaster mantel.  (Washington Post)
She was standing by the fireplace, leaning on the mantel and tapping her fingers, and when she spoke she looked at Eleanor with a bright smile. (The Haunting of Hill House)

Remember, while the word mantle covers many ideas, a mantel is an elegant shelf that goes over the fireplace.