How can reduction in area be used to measure the ductility of a steel bar?

In the context of materials testing, reduction in area is a quantitative measure of a material's ductility—its capacity to undergo permanent deformation under stress.

When a ductile steel bar is subjected to sufficient tensile stress, it does not fracture immediately. Instead, it undergoes a localized deformation known as "necking," where the specimen assumes an hourglass shape. Because the material is ductile, this deformation is permanent and does not recover when the stress is removed.1

To measure ductility using this phenomenon, the reduction in area is calculated as the change in the cross-sectional area of the test section divided by the original area. A greater reduction in the cross-sectional area at the point of necking indicates a higher degree of ductility, as it reflects the material's ability to accommodate significant plastic deformation before reaching the point of fracture.1