Young Modulus
Ratio of stress to strain; measures material stiffness.
Formula
Variables
Example
Steel: ~200 GPa
How it works
Young’s modulus tells you how much a material resists elastic stretching or compression: a larger value means the material deforms less for the same applied stress. It works because, within the elastic limit, many solids show an approximately linear relationship between stress and strain, so their stiffness can be captured by a single ratio. In other words, it compares how much force per area is applied to how much proportional deformation results.
When to use it
Use this formula when you need to compare the stiffness of materials or predict elastic extension/compression in engineering and physics problems. It is especially useful for metals, rods, beams, and wires when the deformation is small enough that the material remains in the elastic region.
Worked example, step by step
A copper rod experiences a stress of 80 MPa and a strain of 4.0 × 10^-4. E = σ / ε E = (80 × 10^6 Pa) / (4.0 × 10^-4) E = 2.0 × 10^11 Pa E = 200 GPa So, the Young modulus of the rod is 200 GPa.
Common mistakes to avoid
- Using force instead of stress; stress must be force divided by cross-sectional area
- Forgetting that strain has no units, so the answer must come out in pascals
- Applying Young’s modulus beyond the elastic limit, where the stress-strain relationship is no longer linear
Did You Know?
A high Young modulus means a stiff, less stretchy material.
Share this formula
More in Materials & Civil
View allStress
BasicInternal force per unit cross-sectional area.
Strain
BasicFractional deformation under load.
Factor of Safety
IntermediateRatio of a material strength to the actual applied stress.
Cantilever Beam Deflection
AdvancedMaximum deflection of a cantilever with an end load.
Rectangular Area Moment of Inertia
AdvancedSecond moment of area for a rectangular cross-section.
Bending Stress
AdvancedStress in a beam due to a bending moment.