Young's Modulus Stress-Strain Calculator
Young's modulus measures how stiff a material is: how much it stretches under a pulling force. It is the slope of the stress-strain curve in the elastic region, where stress is proportional to strain. Engineers use it to predict how much a beam, cable, or component will deflect under load, and to compare candidate materials. Enter the applied force, the cross-sectional area, the original length, and the measured extension; this calculator returns the tensile stress, the strain, and the resulting Young's modulus in both pascals and gigapascals.
Stress, strain and modulus formula
Stress = force / area
Strain = extension / original length
Young's modulus = stress / strain
1 gigapascal = 1,000,000,000 pascals
Force is in newtons, area in square metres, and lengths in metres. Stress comes out in pascals and strain is dimensionless. The modulus equals stress divided by strain, valid only in the linear elastic region.
Material stiffness context
- Young's modulus applies in the linear elastic region where Hooke's law holds and deformation is reversible.
- Typical values: steel about 200 GPa, aluminium 69 GPa, copper 117 GPa, concrete 30 GPa, oak 11 GPa.
- Stress is force spread over area, so a thinner sample carries higher stress for the same force.
- Strain is a pure ratio; a strain of 0.001 means a 0.1 percent change in length.
- Beyond the yield point materials deform plastically and the constant-modulus relationship breaks down.
Young's modulus: frequently asked questions
What is Young's modulus?
Young's modulus is the ratio of tensile stress to tensile strain in the elastic region of a material. It equals stress divided by strain (E = stress / strain) and measures stiffness. The SI unit is the pascal, but values are usually quoted in gigapascals (GPa).
What is the difference between stress and strain?
Stress is force per unit cross-sectional area, in pascals. Strain is the fractional change in length, the extension divided by the original length, and is dimensionless. Young's modulus links the two: stress equals modulus times strain in the elastic region.
What are typical Young's modulus values?
Structural steel is about 200 GPa, aluminium about 69 GPa, concrete about 30 GPa, oak wood roughly 11 GPa, and rubber under 0.1 GPa. Higher modulus means a stiffer material that deforms less under a given stress.
Does this only apply in the elastic region?
Yes. Young's modulus describes linear elastic behaviour where stress is proportional to strain (Hooke's law) and the material returns to its original shape when unloaded. Beyond the yield point materials deform plastically and the simple ratio no longer holds.
How do I find the extension under a load?
Rearranging the definitions, extension equals force times original length divided by the product of cross-sectional area and Young's modulus (deltaL = F x L / (A x E)). This calculator reports stress, strain, and the modulus from the force, area, original length, and measured extension you enter.
Official sources
- NIST: SI units, the pascal and force quantities (SP 811).
- NIST: Physical Measurement Laboratory (mechanical metrology).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.