Young’s modulus from stress and strain
Young’s modulus is the slope of uniaxial normal stress versus longitudinal strain in a material’s linear elastic range. Stress is force divided by original area, and engineering strain is length change divided by original length.
The simple ratio is not generally valid beyond proportional behavior, for unloading hysteresis, or for materials whose response is nonlinear, anisotropic, viscoelastic, plastic, or strongly temperature dependent.
How to use the elastic modulus calculator
- Choose the unknown: Select modulus, stress, or strain.
- Enter two known values: Use pascals for stress and modulus and decimal strain, not percent.
- Calculate: Review the linear elastic result.
- Check material regime: Confirm the data lie within the proportional region and match loading direction and test conditions.
Formula and variables
Because engineering strain is dimensionless, Young’s modulus has the same unit as stress. This calculator uses pascals.
E = σ/ε- E — Young’s modulus
- Uniaxial linear elastic stiffness (Pa)
- σ — Normal stress
- Axial force divided by original cross-sectional area (Pa)
- ε — Engineering strain
- Length change divided by original length (m/m)
Steel-like tensile example
A specimen has stress 200 MPa at engineering strain 0.001.
- Stress
- 2.0 × 10⁸ Pa
- Strain
- 0.001
- E = 2.0 × 10⁸/0.001
- E = 2.0 × 10¹¹ Pa
Result: Young’s modulus is 200 GPa.
The value is meaningful only if this point lies in the specimen’s linear elastic range.
Understanding your results
Higher modulus means greater axial stiffness
For the same uniaxial stress in the linear region, a higher E produces less strain.
- Modulus is not strength or hardness.
- Use decimal strain: 0.1% equals 0.001.
- Material direction, temperature, and test method can affect measured modulus.
Assumptions
- Loading is uniaxial and deformation is small.
- Stress and strain are in the proportional linear elastic region.
- Inputs use engineering stress and engineering strain.
Limitations
- Does not calculate shear, bulk, tangent, secant, or complex modulus.
- Does not model yielding, plasticity, fracture, creep, viscoelasticity, anisotropy, or temperature effects.
- Not a substitute for material test data or design-code properties.
Common mistakes
- Entering megapascals as pascals without conversion.
- Entering percent strain as a whole number.
- Confusing stiffness with strength.
- Applying one modulus to a composite or anisotropic material in every direction.
Practical use cases
Materials education
Check linear elastic stress–strain calculations.
Preliminary deformation screening
Estimate one uniaxial quantity from verified linear material data.
Frequently asked questions
Is Young’s modulus the same as elastic modulus?
Young’s modulus is the elastic modulus for uniaxial normal loading; shear and bulk moduli describe other deformation modes.
Does a high modulus mean a material is strong?
Not necessarily. Modulus measures elastic stiffness, while strength concerns failure or yielding.
Why must strain be dimensionless?
Engineering strain is a ratio of length change to original length, so compatible length units cancel.
Sources and review
- Stress, Strain, and Elastic Modulus — OpenStax University Physics Volume 1. Accessed 2026-07-13.
Reviewed 2026-07-13.