Young's Modulus Calculator
Young's modulus is the fundamental measure of a material's stiffness - how much it resists deformation when pulled or compressed along one axis. Named after Thomas Young (1807), it is the ratio of applied stress to the resulting strain while the material remains elastic. This calculator determines any one of Young's modulus, stress, strain, force, cross-sectional area, original length, or extension, given the other values. It is used by mechanical engineers selecting materials for load-bearing structures, civil engineers designing beams and columns, and materials scientists characterizing new alloys and composites. The tool also shows how much a bar or rod of given dimensions would extend under a specified axial force.
Young's modulus formula
E = stress / strain = (F / A) / (delta_L / L)
E = (F * L) / (A * delta_L)
stress (sigma) = F / A [Pa]
strain (epsilon) = delta_L / L [dimensionless]
Young's modulus of common materials
- Steel: approximately 200 GPa
- Aluminum alloy: approximately 70 GPa
- Titanium: approximately 116 GPa
- Concrete: approximately 30 GPa
- Glass: approximately 65 GPa
- HDPE plastic: approximately 0.8 GPa
Young's modulus: frequently asked questions
What is Young's modulus?
Young's modulus (E) is a measure of the stiffness of a solid material. It is defined as the ratio of tensile stress to tensile strain within the elastic limit: E = stress / strain = (F/A) / (delta_L / L). A higher modulus means the material is stiffer and deforms less under a given load. Steel has E around 200 GPa; rubber is around 0.01 GPa.
What is the difference between stress and strain?
Stress is the internal force per unit area: sigma = F / A (measured in Pascals or N/m^2). Strain is the fractional change in length: epsilon = delta_L / L (dimensionless). Young's modulus relates the two: sigma = E * epsilon. This relationship holds only within the elastic (linear) region of the stress-strain curve.
What is the elastic limit?
The elastic limit is the maximum stress a material can withstand while still returning to its original shape when the load is removed. Beyond the elastic limit, the material deforms plastically - permanent deformation occurs. Young's modulus only applies below the elastic limit.
What are typical Young's modulus values?
Steel: 200 GPa, Aluminum: 70 GPa, Concrete: 30 GPa, Wood (along grain): 10 GPa, Glass: 65 GPa, Bone: 14 GPa, Rubber: 0.01 to 0.1 GPa. Diamond has the highest known Young's modulus at about 1050 GPa.
How is Young's modulus used in engineering?
Engineers use Young's modulus to calculate deflections of beams, elongation of structural members, spring rates of elastic components, and natural frequencies of structures. It is essential in finite element analysis, structural design, material selection for stiffness-critical applications, and aerospace components where weight-to-stiffness ratio matters.
Official sources
- NIST: NIST Materials Measurement Science Division.
- ASM International: ASM Materials Information.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.