Young's Modulus Calculator
Calculate the modulus of elasticity from stress and strain measurements
Calculate Young's Modulus
Force and Area Inputs
Length Measurements
Young's Modulus Results
Formula used: E = σ / ε
Note: Young's modulus represents the material's stiffness - higher values indicate stiffer materials
Example Calculation
Copper Wire Example
Problem: A copper wire under tensile testing
Cross-sectional area: 0.5 × 0.4 mm = 0.2 mm²
Initial length: 0.500 m
Applied force: 100 N
Final length: 0.502 m
Calculation Steps
1. Area = 0.2 mm² = 0.0000002 m²
2. Stress = F/A = 100 N / 0.0000002 m² = 5×10⁸ Pa
3. Strain = (L-L₀)/L₀ = (0.502-0.500)/0.500 = 0.004
4. E = σ/ε = 5×10⁸ Pa / 0.004 = 1.25×10¹¹ Pa = 125 GPa
Result: Close to copper's typical value of ~130 GPa
Common Material Properties
Diamond
~1200 GPa
Hardest natural material
Steel
~200 GPa
Common structural material
Wood
~10 GPa
Natural composite material
Young's Modulus Tips
Higher values indicate stiffer materials
Only valid in the elastic (linear) region
Units are the same as stress (Pa, MPa, GPa)
Independent of object size and shape
Understanding Young's Modulus
What is Young's Modulus?
Young's modulus (E), also called the modulus of elasticity, is a fundamental mechanical property that measures a material's stiffness. It represents the relationship between stress (force per unit area) and strain (deformation) in the elastic region.
Why is it Important?
- •Predicts how much a material will deform under load
- •Essential for structural engineering design
- •Helps select appropriate materials for applications
- •Intrinsic material property (size-independent)
Formula and Units
E = σ / ε
E = (F/A) / ((L-L₀)/L₀)
- E: Young's modulus (Pa, GPa)
- σ: Stress (Pa)
- ε: Strain (dimensionless)
- F: Applied force (N)
- A: Cross-sectional area (m²)
- L₀: Initial length (m)
- L: Final length (m)
Note: Young's modulus is only valid in the elastic region where stress and strain have a linear relationship.