Elastic Modulus Calculator Formula
Understand the math behind the elastic modulus calculator. Each variable explained with a worked example.
Formulas Used
Elastic Modulus (E)
modulus_gpa = stress / strain / 1000Elastic Modulus
modulus_mpa = stress / strainVariables
| Variable | Description | Default |
|---|---|---|
stress | Stress (sigma)(MPa) | 200 |
strain | Strain (epsilon) | 0.001 |
How It Works
Young's Modulus (Elastic Modulus)
Young's modulus E is the slope of the linear portion of the stress-strain curve. It measures a material's stiffness, or resistance to elastic deformation.
Formula
E = sigma / epsilon
where sigma is the axial stress and epsilon is the axial strain (both in the elastic region). E is an intrinsic material property independent of geometry.
Worked Example
A steel specimen shows 200 MPa stress at 0.001 strain (0.1%) in the elastic region.
- 01E = 200 MPa / 0.001
- 02E = 200,000 MPa = 200 GPa
- 03This is consistent with structural steel (E ≈ 200 GPa)
Frequently Asked Questions
What are typical elastic modulus values?
Steel: ~200 GPa, aluminum: ~70 GPa, copper: ~120 GPa, titanium: ~110 GPa, concrete: ~30 GPa, wood (along grain): ~10-15 GPa, rubber: ~0.01-0.1 GPa.
Does temperature affect the elastic modulus?
Yes. Elastic modulus generally decreases with increasing temperature. For steel, E drops about 5% per 100°C. At very high temperatures (near melting), the reduction is much more significant.
What is the relationship between E, G, and Poisson's ratio?
For isotropic materials: G = E / (2(1 + nu)), where G is shear modulus and nu is Poisson's ratio. This means knowing any two of these three properties determines the third.
Ready to run the numbers?
Open Elastic Modulus Calculator