Young's Modulus Calculator
Calculate Young's modulus (E) from stress and strain
Normal stress (tensile or compressive) in the elastic region
Normal strain corresponding to the stress (in elastic region)
How to Use This Calculator
Enter Stress
Input the normal stress (σ) in MPa or psi. This should be measured in the elastic (linear) region of the stress-strain curve, before plastic deformation occurs. Stress can be tensile (positive) or compressive (negative).
Enter Strain
Input the normal strain (ε) corresponding to the stress. Strain is dimensionless and typically very small (e.g., 0.001 = 0.1%). Make sure the stress and strain are from the same test point in the elastic region.
Calculate Young's Modulus
Click "Calculate" to determine Young's modulus (E). This value represents the material's stiffness in the elastic region and is a fundamental material property. The result will be in the same stress units as your input (MPa or psi).
Formula
Young's Modulus = Stress ÷ Strain
E = σ / ε
Where:
- E = Young's modulus (elastic modulus) - MPa, GPa, or psi
- σ = Normal stress - MPa or psi
- ε = Normal strain - dimensionless
Hooke's Law:
In the elastic region, stress is proportional to strain: σ = E × ε. This linear relationship is valid only for small deformations within the elastic limit. Young's modulus is the slope of the stress-strain curve in this linear region.
Example:
For stress 200 MPa and strain 0.001:
E = 200 ÷ 0.001 = 200,000 MPa = 200 GPa
This is typical for steel.
About Young's Modulus Calculator
The Young's Modulus Calculator is an essential tool for materials engineering and mechanical design that calculates Young's modulus (E), also known as the elastic modulus or tensile modulus. Young's modulus is a fundamental material property that quantifies a material's stiffness and resistance to elastic deformation under uniaxial loading.
When to Use This Calculator
- Material Testing: Calculate E from tensile or compression test data
- Material Selection: Compare stiffness properties of different materials
- Design Calculations: Determine material stiffness for structural analysis
- Research & Development: Characterize new materials or material treatments
- Quality Control: Verify material properties meet specifications
Why Use Our Calculator?
- ✅ Simple Calculation: Quick E from stress and strain measurements
- ✅ Fundamental Property: Essential material stiffness parameter
- ✅ Design Tool: Critical for structural and mechanical design
- ✅ Educational Resource: Understand elastic modulus concepts
- ✅ Accurate Results: Precise calculations from test data
Key Concepts
Young's Modulus (E): Also called elastic modulus or tensile modulus, Young's modulus is a measure of a material's stiffness in the elastic region. It represents the ratio of stress to strain: E = σ/ε, and is the slope of the linear portion of the stress-strain curve. Higher E values indicate stiffer materials that deform less under the same stress. E is a fundamental material property that depends on atomic bonding and microstructure, not geometry.
Elastic Deformation: Young's modulus applies only to elastic (reversible) deformation, where stress and strain have a linear relationship (Hooke's law: σ = E × ε). Once stress exceeds the elastic limit (yield strength), the material deforms plastically and the linear relationship no longer holds. Therefore, stress and strain values used to calculate E must be from the elastic region.
Typical Young's Modulus Values
- Steel: 200 GPa (29,000 ksi)
- Aluminum: 70 GPa (10,000 ksi)
- Copper: 110 GPa (16,000 ksi)
- Concrete: 20-40 GPa (3,000-6,000 ksi)
- Wood (along grain): 8-15 GPa (1,200-2,200 ksi)
- Rubber: 0.01-0.1 GPa (1.5-15 ksi)
Frequently Asked Questions
What is Young's modulus?
Young's modulus (E), also called elastic modulus or tensile modulus, is a fundamental material property that measures a material's stiffness in the elastic region. It is defined as E = σ/ε, the ratio of stress to strain in the linear elastic region. Higher E values indicate stiffer materials that deform less under applied stress. Young's modulus is a material property (not geometry-dependent) and is essential for predicting material behavior under load.
Why is Young's modulus important?
Young's modulus is important because it quantifies material stiffness, which affects how much a component deforms under load. It's essential for: 1) Structural design (predicting deflections), 2) Material selection (choosing appropriate stiffness), 3) Finite element analysis (required material input), 4) Stress-strain calculations (σ = E × ε), 5) Comparing material properties. A higher E means less deformation for the same stress, which is often desirable for structural applications.
Can I use stress-strain data from the plastic region?
No, Young's modulus should only be calculated using stress-strain data from the elastic (linear) region. Once the material yields and enters the plastic region, the linear relationship (σ = E × ε) no longer holds. Using plastic region data would give an incorrect (and typically much lower) apparent modulus. Always use stress-strain pairs from the initial linear portion of the curve, before yield occurs.
Does Young's modulus depend on material geometry?
No, Young's modulus (E) is a material property and does not depend on geometry. It depends only on material composition, microstructure, and atomic bonding. However, the actual deformation (strain) for a given load does depend on geometry (e.g., longer or thinner samples deform more). This is why stiffness (force/displacement) depends on geometry, but Young's modulus (stress/strain) does not.
How does Young's modulus relate to other elastic constants?
Young's modulus (E), shear modulus (G), bulk modulus (K), and Poisson's ratio (ν) are related for isotropic materials: E = 2G(1 + ν) and E = 3K(1 - 2ν). If you know any two, you can calculate the others. For most metals, ν ≈ 0.3, so E ≈ 2.6G. Young's modulus describes uniaxial tension/compression, shear modulus describes shear deformation, and bulk modulus describes volumetric compression.