In architecture, a cupola is a dome-shaped ornamental structure located on top of a larger roof or dome, often used as a lookout or to admit light and air. In some cases, the entire main roof of a tower or spire can be a cupola. More frequently, however, the cupola is a smaller structure which sets on top of the main roof. One can often reach the cupola by climbing a stairway inside the building; this type of accessible cupola is called a belvedere or a widow's walk. Some cupolas, called lanterns, have small windows which illuminate the areas below.
Cupolas are also found on tracked, armored vehicles, where they are used as protected observation posts.
A cupola is a cylindrical shaft type of blast furnace used for remelting metals, usually iron, before casting.
In mathematics, a cupola is a solid formed by joining two polygons, one (the base) with twice as many faces as the other, by an alternating band of triangles and rectangles. The triangular, square, and pentagonal cupolae all count among the Johnson solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively.