Modulus of Resilience Calculator

About this calculator

The modulus of resilience (Ur) is a materials-science property equal to the elastic strain energy a material can absorb per unit volume before it starts to permanently deform, calculated as Ur = σy²/(2E) — the yield strength squared divided by twice the Young's modulus. Graphically, it's the area under the stress-strain curve up to the yield point, representing energy the material returns fully once the load is removed.

Engineers use this property to select materials for applications that must absorb shock or store elastic energy without yielding — springs, bumpers, and impact-resistant components, for example, favor materials with a high modulus of resilience even if their overall strength or stiffness isn't the highest available. It's a standard calculation in mechanical and materials engineering coursework and in selecting alloys for fatigue-and-impact-sensitive parts.