Roundness

Roundness is a measure of how closely a shape resembles a circle in two dimensions, or, for three-dimensional bodies, how close the shape is to a sphere. In practical terms, roundness describes the smoothness of a shape’s outline or surface, with perfectly round objects exhibiting minimal angularity and sharp corners.

In geometry and image analysis, a common 2D measure is circularity, defined as 4πA/P^2, where A is the area and P is the perimeter. Circularity equals 1 for a circle and falls below 1 as shapes become less circular. This metric emphasizes the overall footprint of a shape rather than local edge features.

In geology and materials science, “roundness” is often used to describe how smooth the edges and corners of a particle are. This Wadell-style roundness focuses on the degree of edge rounding rather than the overall silhouette. It is distinct from circularity (a 2D concept) and from sphericity, which assesses how closely a three-dimensional particle matches a sphere.

Measurement methods vary by discipline. 2D roundness is commonly estimated from digital images through contour extraction and area–perimeter calculations. 3D roundness or sphericity may use 3D scanning, CT imaging, or stereovision to compare a particle’s shape to a sphere.

Applications span quality control in manufacturing, mineral and pharmaceutical processing, sedimentology, and planetary science. Because different definitions exist, it is important to specify the exact method used when reporting roundness.