Young’s Modulus Calculator:
Enter the values of stress, S1(Pa) and strain, S2 to determine the value of Young’s Modulus, Y(Pa).
Young’s Modulus Formula:
Young’s Modulus (Y), also called the modulus of elasticity, is a measure of a material’s stiffness or resistance to deformation under stress. It defines the relationship between stress (force per unit area) and strain (relative deformation) in a material when subjected to axial forces.
The material obeys Hooke’s Law in this elastic region, meaning stress is proportional to strain. Young’s Modulus is fundamental in engineering and material science for determining how materials will deform under load.
It is expressed as the ratio of stress (S) to strain (e), where stress is the force applied over an area, and strain is the resulting deformation per unit length. A higher Young’s Modulus indicates the material is stiffer and less elastic. Materials like steel have high values, while rubber has a low Young’s Modulus.
The unit of Young’s Modulus is Pascals (Pa), or N/m2 in the SI system, and it is a constant for a given material under elastic deformation.
Young’s Modulus, Y(Pa) in Pascals equals stress, S1(Pa) in Pascals divided by strain, S2.
Young’s Modulus, Y(Pa) = S1(Pa) / S2
Y(Pa) = Young’s Modulus in Pascals, Pa.
S1(Pa) = stress in Pascals, Pa.
S2 = strain.
Young’s Modulus Calculation:
1.A metal rod with an original length of 1 m is stretched by applying a force of 100 N. The cross-sectional area of the rod is 0.01 m2, and the elongation (ΔL) observed is 0.002 m. Calculate the Young’s Modulus of the rod.
Given: F(N) = 100 N, A(m2) = 0.01 m2, L(m) = 1 m, ΔL(m) = 0.002 m.
Young’s Modulus, Y(Pa) = S1(Pa) / S2
S1(Pa) = F(N) / A(m2) = 100 / 0.01 = 10000Pa.
S2 = ΔL(m) / L(m) = 0.002 / 1 = 0.002.
Y(Pa) = 10000 / 0.002
Y(Pa) = 5000000Pa.
2.A wire experiences stress S1 = 2000 Pa and Young’s Modulus of the wire is 2000000Pa. Find strain.
Given: S1(Pa) = 2000 Pa, Y(Pa) = 2000000Pa.
Young’s Modulus, Y(Pa) = S1(Pa) / S2
S2 = S1(Pa) / Y(Pa)
S2 = 2000 / 2000000
S2 = 0.001.