Stress Strain Calculator
Four Ways Into the Same Relationship
Stress, strain, and the elastic modulus that connects them form the foundation of how engineers predict whether a part deforms safely or fails. Depending on what's known and what's being solved for, the useful starting point changes — sometimes it's a measured force and area, sometimes a measured deformation, and sometimes the material property itself. This calculator covers all four directions.
The Formulas
Strain: ε = Change in Length / Original Length
Elastic Modulus (Hooke's Law): E = σ / ε
Stress from Modulus: σ = E × ε
Hooke's Law only holds within a material's elastic region — below its yield point, where deformation is fully recoverable once the load is removed.
Worked Examples
| Mode | Inputs | Result |
|---|---|---|
| Stress | 5,000 N over 100 mm² | 50.0 MPa |
| Strain | 0.5 mm change over 500 mm original length | 0.001 |
| Elastic Modulus | 50 MPa stress at 0.001 strain | 50.0 GPa |
The strain and modulus examples here are linked: a material with the strain result above (0.001) under 50 MPa of stress has an elastic modulus of 50 GPa, and running that same modulus and strain back through the fourth mode returns the original 50 MPa stress.
Where This Calculation Matters
- Material verification — back-calculating elastic modulus from a measured stress-strain pair to confirm a material matches its specification.
- Deflection prediction — using a known modulus and applied stress to predict how much a component will stretch or compress under load.
- Cross-checking test data — converting raw force and deformation measurements from a tensile test into engineering stress and strain values.
How to Use This Calculator
- Choose the mode: Stress (Force / Area), Strain (Change in Length), Elastic Modulus (Stress / Strain), or Stress from Modulus × Strain.
- For stress, enter Force (N) and Cross-Sectional Area (mm^2).
- For strain, enter Change in Length (mm) and Original Length (mm).
- For elastic modulus, enter Stress (MPa) and Strain (dimensionless).
- For stress from modulus, enter Elastic Modulus (GPa) and Strain (dimensionless).
- Select Calculate to get the result for the chosen mode.
Related Calculations
For stress under cyclic rather than static loading, move on to the Fatigue Life Calculator.