What does concavity mean?
Concavity refers to the state or degree of being concave — that is, curving inward like the inner surface of a bowl or cave. The word names both an abstract quality and, in its plural form, actual hollow or sunken regions: the concavities of a landscape, a sculpture, or a machined part. It appears most often in technical and academic contexts. In mathematics, especially calculus, concavity describes how a curve bends: a graph is 'concave up' where it opens upward and 'concave down' where it opens downward, a property determined by the sign of the second derivative. Engineers and designers invoke concavity when discussing lenses, mirrors, dishes, and surfaces shaped to focus light, sound, or signals. Its everyday counterpart is far simpler — any dent, dip, or hollow exhibits concavity. The natural opposite is convexity, the quality of bulging outward. Precise but not obscure, concavity gives speakers a compact way to describe curvature without resorting to loose words like 'bend' or 'dip'.
The state or quality of being concave; the amount or degree to which a surface or curve bends inward.
"Mathematicians analyze the concavity of a graph by examining its second derivative."
In calculus, 'concavity' specifically describes whether a function's graph lies above or below its tangents.
A hollow, depression, or inwardly curved surface or region; usually expressed in the plural 'concavities'.
"Erosion carved deep concavities into the cliff face over centuries."
The plural typically denotes multiple distinct hollow or inward-curved areas, such as those on a physical object or landscape.
"The sculptor polished every concavity until it reflected light evenly."
Flip a bowl over and you've turned its concavity into convexity — same shape, opposite personality.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of concavity
Concavity derives from Latin 'concavus,' meaning 'hollow' or 'arched inward,' formed from the prefix 'con-' (here intensifying) and 'cavus' ('hollow'), the same root that gives us 'cave' and 'cavity.' The word entered English in the late 16th to early 17th century, when scientific and mathematical vocabulary was expanding rapidly through borrowing from Latin. Its sibling term 'convexity,' from the Latin 'convexus' ('arched outward'), developed alongside it as the standard antonym.
Related word forms
How concavity is actually used
Concavity is a formal, largely technical term, most at home in mathematics (where 'concavity' of a function is a standard topic in calculus), geometry, physics, and descriptions of physical surfaces. In everyday speech people more often say something 'is concave' than refer to 'its concavity.' The plural 'concavities' typically refers to multiple distinct hollows or curved regions rather than an abstract quality.
Easily confused with concavity
Convexity describes a surface that curves outward like the outside of a sphere, whereas concavity describes one that curves inward like the inside of a bowl.