Quick answer
Young's modulus E = stress ÷ strain in the linear elastic region. A stress of 250 MPa producing a strain of 0.0012 gives E = 208.33 GPa, close to steel.
Enter stress and strain. The calculator returns the modulus.
Related tools: Moment of Inertia Calculator: Area moment of inertia of common cross-sections.
How to use the Young's Modulus Calculator
- Enter stress (MPa) (above 0).
- Enter strain (dimensionless) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Stress | A number, in MPa | > 0 |
| Strain (dimensionless) | A number | > 0 |
Formula and method
Formula
E = σ ÷ ε
IEEE-754 double precision; shown to the decimals indicated.
Valid in the linear elastic range.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Stress = 250; Strain (dimensionless) = 0.0012.
| Result | Value |
|---|---|
| Young's modulus | 208.3333 GPa |
Example 2
Inputs: Stress = 120; Strain (dimensionless) = 0.0016.
| Result | Value |
|---|---|
| Young's modulus | 75 GPa |
Example 3
Inputs: Stress = 400; Strain (dimensionless) = 0.002.
| Result | Value |
|---|---|
| Young's modulus | 200 GPa |
The first line is the headline result (young's modulus). IEEE-754 double precision; shown to the decimals indicated.
Typical moduli
Steel is about 200 GPa, aluminium 70 GPa, copper 117 GPa, concrete 25 to 40 GPa, wood 10 to 15 GPa along the grain and rubber under 0.1 GPa. A higher modulus means a stiffer material.
Linear region only
The relationship holds only in the linear elastic range. Beyond the yield point the stress-strain curve is no longer straight. Read both values from the straight part of the curve.
How the result changes with stress
Holding every other input at the first worked example, this table changes only stress. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Stress | Young's modulus |
|---|---|
| 125 | 104.1667 GPa |
| 250 | 208.3333 GPa |
| 500 | 416.6667 GPa |
| 1000 | 833.3333 GPa |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Stress: entering "0" shows "Stress must be greater than 0." beside that field and no result.
- Strain (dimensionless): entering "0" shows "Strain (dimensionless) must be greater than 0." beside that field and no result.
Choosing between the Young's Modulus Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Beam Deflection Calculator](/engineering/beam-deflection-calculator/) | beam and load, load and span | Maximum deflection |
| [Moment of Inertia Calculator](/engineering/moment-of-inertia/) | section and dimension a | Moment of inertia (Ix) |
| [Beam Bending Stress Calculator](/engineering/beam-bending-stress-calculator/) | bending moment, distance from neutral axis and second moment of area | Bending stress |
| [Column Buckling Calculator](/engineering/column-buckling-calculator/) | modulus of elasticity, smallest second moment of area and column length | Critical load |
| [Factor of Safety Calculator](/engineering/factor-of-safety-calculator/) | strength or capacity and applied load or stress | Factor of safety |
Background: structural and wiring estimates
Structural and electrical results are only as good as their assumptions. Bending stress is the bending moment divided by the section modulus, and an allowable stress is the yield strength divided by a safety factor that depends on the governing design code and the type of load. For a single-phase or DC run the voltage drop uses the round-trip length: V = 2 × L × R per unit length × I.
Recommended limits, such as keeping branch-circuit voltage drop around 3%, differ between sources and code editions. These pages are estimates: follow the applicable code and a qualified engineer or electrician for real work.
Assumptions and limitations
- Linear elastic region only
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for stress and strain (dimensionless) to confirm this.
Frequently asked questions
What is the unit of Young's modulus?
Pascals, usually GPa for metals.
Is stiffness the same as strength?
No, stiffness is resistance to deformation.
How do I measure it?
From a tensile test.
What does the Young's Modulus Calculator calculate?
Modulus of elasticity from stress and strain. It returns Young's modulus.
What formula does the Young's Modulus Calculator use?
E = σ ÷ ε. Valid in the linear elastic range.
What do I need to enter in the young's Modulus Calculator?
You enter Stress (MPa) and Strain (dimensionless).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Linear elastic region only.
What is an example of a young's Modulus result?
With stress 250 and strain (dimensionless) 0.0012, the young's modulus is 208.3333 GPa.
Where does the method come from?
The method follows: Hooke's law (e.g. Gere & Goodno).
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Linear elastic region only.
Related calculators
- Moment of Inertia Calculator — Area moment of inertia of common cross-sections.
- Strain Calculator — Engineering strain from change in length.
Sources
- Hooke's law (e.g. Gere & Goodno)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.