How to use Hooke’s law for stress
For a linearly elastic material, stress and strain grow in proportion. Young’s modulus E describes stiffness: a stiffer material needs more stress to reach the same strain.
What the formula is saying
Rearrange E = stress / strain to stress = E × strain. This is a straight-line material model; it is not a rule that all materials obey at every load.
Read the symbols in plain language
- E
- Young’s modulusPa
- ε
- Strainratio / no unit
Sort out the units first
Enter E in Pa. 200 GPa = 200,000,000,000 Pa. Enter 0.0005 for 0.05% strain. A dimensionless strain leaves the answer in Pa.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- E · Young’s modulus
- 200000000000 Pa
- ε · Strain
- 0.0005
Express stiffness in pascals
Giga means one billion, so convert GPa before multiplying.
(200000000000) = 200000000000 PaMultiply by the strain ratio
The strain is already a ratio; do not divide it by 100 again.
(200000000000) × (0.0005) = 100000000 Pa
Does this worked answer make sense?
Halving strain halves stress when E stays fixed. The example gives 100 MPa, an output of this model rather than a safety approval.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- E · Young’s modulus
- 70000000000 Pa
- ε · Strain
- 0.001
Find: How to use Hooke’s law for stress
A hint, not the answer
Rearrange E = stress / strain to stress = E × strain. This is a straight-line material model; it is not a rule that all materials obey at every load.
Enter E in Pa. 200 GPa = 200,000,000,000 Pa. Enter 0.0005 for 0.05% strain. A dimensionless strain leaves the answer in Pa.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Express stiffness in pascals
Giga means one billion, so convert GPa before multiplying.
(70000000000) = 70000000000 PaMultiply by the strain ratio
The strain is already a ratio; do not divide it by 100 again.
(70000000000) × (0.001) = 70000000 Pa
Avoid the common trap
Using E = 200 with a Pa output loses a factor of one billion. Do not confuse stiffness E with yield strength.
When this method applies — and when it does not
Use only in the linearly elastic range with the relevant modulus. This lesson does not check yielding, cracking, or nonlinear response.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.