What is a Pendentive? Dome Engineering

Historic Solution to Higher Domes

Interior of Paris Pantheon dome shows 18th century pendentives next to illustration of pendentives
The Dome of the Paris Pantheon Illustrates Pendentives Structurally and Artistically. Left photo by Chesnot / Getty Images News / Getty Images (cropped) / Right Illustration by Encyclopaedia Britannica/UIG Universal Images Group/Getty Images

A pendentive is a method for stabilizing a round dome on a square frame, resulting in enormous interior open space beneath the dome. Specifically, a pendentive is the triangular piece, usually ornamented, that makes a dome appear as if it's hanging in the air, like a "pendent."

How did early structural engineers design round domes to be supported over square buildings? Builders in 500 AD used pendentives to create additional height and carry the weight of domes in Early Christian architecture of the Byzantine era.

Don't worry if you just can't visualize this engineering. It took civilization hundreds of years to figure out the geometry and physics. Let's look at how others define the pendentive.

What is a Pendentive?

"A triangular spheroid section used to effect the transition from a square or polygonal base to a dome above."—G. E. Kidder Smith
"One of a set of curved wall surfaces which form a transition between a dome (or its drum) and the supporting masonry."—Dictionary of Architecture and Construction

The Geometry of Pendentives:

Although Romans experimented with pendentives early on, the structural use of pendentives was an Eastern idea for Western architecture. "It was not until the Byzantine period and under the Eastern Empire that the enormous structural possibilities of the pendentive were appreciated," says Professor Talbot Hamlin, FAIA. To support a dome over the corners of a square room, builders realized that the diameter of the dome had to equal the diagonal of the room and not its width.

Professor Hamlin explains:

"To understand the form of a pendentive, it is only necessary to place half an orange with its flat side down on a plate and cut equal portions vertically off the sides. What is left of the original hemisphere is called a pendentive dome. Each vertical cut will be in the shape of a semicircle. Sometimes these semicircles were built as independent arches to support the upper spherical surface of the dome. If the top of the orange is cut off horizontally at the height of the top of these semicircles, the traingular pieces still left will be exactly the shape of pendentives. This new circle can be made the base for a new complete dome, or a vertical cylinder can be built upon it to support another dome higher up."—Talbot Hamlin

Why are Pendentives Significant in Architecture?

  1. New engineering techniques allowed interior domes to rise to new heights.
  2. Pendentives created a geometrically interesting interior space to be ornamented. Four pendentive areas could tell a visual story.
  3. Pendentives tell the real story of architecture. Architecture is about solving problems—for example, how to create soaring interiors that expresses man's adoration of God. Architecture also evolves over time. We say that architects build on each other's discoveries, which makes the art and craft an "iterative" process of evolution. Many, many domes fell down into a crumble of ruin before the mathematics of geometry solved the problem. Pendentives allowed domes to soar and gave artists another canvas.

Examples of Pendentives:

Sources: Source Book of American Architecture, G. E. Kidder Smith, Princeton Architectural Press, 1996, p. 646; Dictionary of Architecture and Construction, Cyril M. Harris, ed., McGraw- Hill, 1975, p. 355; Architecture through the Ages by Talbot Hamlin, Putnam, Revised 1953, pp. 229-230