Calculation
E = σ / ε
E is the slope of the stress-strain curve; high values mean high stiffness.
E = σ/ε
Young's Modulus Calculator
E is the slope of the stress-strain curve; high values mean high stiffness.
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Result
Select a target and calculate.
Understand the inputs
- Young's modulus E — Young's modulus – the material stiffness in the linear-elastic range (Hooke's law). High values mean a given stress produces only a small strain. Source: material table (typical values: steel ≈ 210 GPa, aluminium ≈ 70 GPa); determine it yourself from σ/ε only for unknown materials.
- Normal stress σ — The stress at the considered load point, computed from F/A or measured; must lie in the linear-elastic range, i.e. below the material's yield strength.
- Strain ε — The corresponding strain (as a fraction, not a percentage) at the same load as σ. Source: a strain gauge or an extensometer.
Example
200 MPa / 0.001 = 200 GPa.
Assumptions and limits
Linear-elastic, isotropic material under uniaxial load.
Understand Young's Modulus Calculator
This calculator finds the missing quantity among Young's modulus E, normal stress σ and strain ε from the other two, within a material's linear-elastic range. Using the huge stiffness gap between steel, aluminium and rubber, it shows why the same applied stress produces wildly different deformation depending on material.
What does this quantity describe?
Young's modulus describes a material's stiffness in the linear-elastic range as the ratio of stress to strain: E = σ/ε. It is the slope of the stress-strain curve and a pure material constant, independent of part size.
Steel has a Young's modulus of about 200 GPa, roughly three times aluminium's (about 69 GPa) and thousands of times rubber's (about 0.01-0.1 GPa). That's why a steel ruler barely deflects under a given bending force, while an identically shaped piece of rubber bends immediately and visibly — under the exact same applied stress.
Formula and variables
E = σ / ε
E = σ / εσ = E · εε = σ / E
| Symbol / input | Meaning |
|---|---|
| Young's modulus E | Young's modulus – the material stiffness in the linear-elastic range (Hooke's law). High values mean a given stress produces only a small strain. Source: material table (typical values: steel ≈ 210 GPa, aluminium ≈ 70 GPa); determine it yourself from σ/ε only for unknown materials. |
| Normal stress σ | The stress at the considered load point, computed from F/A or measured; must lie in the linear-elastic range, i.e. below the material's yield strength. |
| Strain ε | The corresponding strain (as a fraction, not a percentage) at the same load as σ. Source: a strain gauge or an extensometer. |
Choose the inputs correctly
Enter two of the three quantities. Young's modulus requires stress and strain, stress requires modulus and strain, strain requires modulus and stress. The formula applies only in the linear-elastic range, below the material's yield strength.
How to use the calculator
Select the target quantity and enter the two known values with units. When deriving E from a tensile test, check that the stress and strain values used actually come from the initial linear part of the curve.
Worked example
Given σ = 200 MPa and ε = 0.001, substitution gives E = 200 MPa/0.001 = 200,000 MPa = 200 GPa, a typical value for structural steel.
Understand the result and units
A modulus of 200 GPa means, by linear extrapolation, that 200,000 MPa of stress would in principle be needed to reach 100% strain — in reality the material fractures long before that. Practically, Young's modulus mainly shows how stiff a part behaves under load: a high modulus means low deformation for a given stress.
Young's modulus is given in pascals (Pa), typically GPa in engineering, since values for common structural materials span tens to hundreds of GPa. 1 GPa = 1,000 MPa = 1,000 N/mm².
Typical applications
Young's modulus is used to design components for allowable deflection, calculate spring rates, verify deformation in structural engineering, and compare materials for stiffness-critical applications such as vehicle frames or aircraft structures.
Assumptions, limits and common mistakes
The formula applies only in the linear-elastic range below yield strength, where the part fully returns to shape after unloading. Above yield, plastic deformation sets in and the stress-strain relationship is no longer linear; the modulus calculated here no longer describes real part behaviour in that regime.
Common mistake: Do not confuse Young's modulus with yield strength or tensile strength: modulus describes stiffness (resistance to elastic deformation), while yield strength describes the load level at which permanent deformation begins. Two materials can share the same modulus but have very different yield strengths, or vice versa.
Frequently asked questions
Why does a steel ruler bend less than an identically sized rubber ruler?
Because steel's modulus, about 200 GPa, is thousands of times rubber's (about 0.01-0.1 GPa). At the same applied stress, rubber's strain is correspondingly much larger.
Is a high Young's modulus always better?
Not inherently — it depends on the application. Stiff, shape-stable parts want a high modulus, while springs, seals or shock-absorbing elements need a low one.
What is the difference between Young's modulus and yield strength?
Modulus describes stiffness in the elastic range; yield strength describes the stress at which permanent (plastic) deformation begins. Both are independent material properties.