True Strain Calculator
Calculate true strain and engineering strain
How to Use This Calculator
Enter Initial Length
Input the original or initial length (L₀) of the specimen before deformation. This is the reference length used for strain calculations. Use consistent units (mm or inches).
Enter Final Length
Input the final length (L_f) after deformation. For tensile tests, this is the length after elongation. For compression tests, this is the shorter length after compression. Use the same units as initial length.
Calculate Strains
Click "Calculate" to determine both true strain and engineering strain. True strain uses logarithmic calculation and is more accurate for large deformations. Engineering strain is the simpler approximation.
Formulas
True Strain (Logarithmic Strain)
ε_true = ln(L_f / L₀)
Accurate for all deformation levels, accounts for changing reference length
Engineering Strain (Nominal Strain)
ε_eng = (L_f - L₀) / L₀
Simple approximation, valid for small deformations only
Where:
- ε_true = True strain (dimensionless)
- ε_eng = Engineering strain (dimensionless)
- L₀ = Initial length - mm or in
- L_f = Final length - mm or in
- ln = Natural logarithm
Relationship:
ε_true = ln(1 + ε_eng)
For small strains (ε_eng < 0.05), true strain ≈ engineering strain
About True Strain Calculator
The True Strain Calculator is an essential tool for materials engineering that calculates true strain (also called logarithmic strain) and engineering strain from length measurements. True strain is more accurate for large deformations and is preferred in plasticity theory and finite deformation analysis.
When to Use This Calculator
- Material Testing: Calculate strain from tensile or compression test data
- Plasticity Analysis: Use true strain for large deformation problems
- Finite Element Analysis: Convert measurements to true strain for FEA input
- Research & Development: Analyze deformation behavior accurately
- Quality Control: Verify material deformation characteristics
Why Use Our Calculator?
- ✅ Accurate Calculation: True strain for large deformations
- ✅ Dual Output: Provides both true and engineering strain
- ✅ Material Testing: Essential for deformation analysis
- ✅ Educational Resource: Understand strain concepts
- ✅ Quick Results: Instant calculations from length measurements
Key Concepts
True Strain (Logarithmic Strain): A measure of deformation that accounts for the changing reference length during deformation. It is calculated as the natural logarithm of the length ratio: ε_true = ln(L_f/L₀). True strain is additive for sequential deformations and is preferred for large deformations and plasticity analysis.
Engineering Strain: A simpler approximation that uses the original length as a constant reference: ε_eng = (L_f - L₀)/L₀. Engineering strain is valid only for small deformations (typically < 5%). For large deformations, engineering strain becomes inaccurate because it doesn't account for the changing reference length.
Key Differences
- Accuracy: True strain is accurate for all deformation levels; engineering strain only for small deformations
- Additivity: True strain is additive; engineering strain is not
- Reference: True strain uses instantaneous length; engineering strain uses original length
- Applications: True strain for plasticity and large deformations; engineering strain for elastic analysis
Frequently Asked Questions
What is true strain?
True strain (ε_true), also called logarithmic strain, is a measure of deformation calculated as ε_true = ln(L_f/L₀), where L₀ is initial length and L_f is final length. Unlike engineering strain, true strain accounts for the changing reference length during deformation, making it accurate for all deformation levels, especially large deformations.
What's the difference between true strain and engineering strain?
Engineering strain uses the original length as a constant reference: ε_eng = (L_f - L₀)/L₀. True strain uses logarithmic calculation: ε_true = ln(L_f/L₀), accounting for changing reference length. Engineering strain is valid only for small deformations (< 5%), while true strain is accurate for all deformation levels. True strain is also additive (total strain = sum of increments), while engineering strain is not.
When should I use true strain vs. engineering strain?
Use true strain for: large deformations (> 5%), plasticity analysis, finite deformation problems, sequential loading, and material models requiring accurate strain measures. Use engineering strain for: small deformations (< 5%), elastic analysis, simple calculations, and when initial length is the only reference available. For most metal forming and large deformation problems, true strain is preferred.
Why is true strain additive?
True strain is additive because it uses instantaneous length as the reference. If you deform from L₀ to L₁, then L₁ to L₂, the total true strain equals the sum: ε_total = ln(L₁/L₀) + ln(L₂/L₁) = ln(L₂/L₀). Engineering strain is not additive because it always uses the original length, so sequential engineering strains can't simply be added.
How do I convert engineering strain to true strain?
Convert engineering strain (ε_eng) to true strain (ε_true) using: ε_true = ln(1 + ε_eng). For small strains (ε_eng < 0.05), they are approximately equal. For example, if engineering strain is 0.1 (10%), true strain = ln(1.1) = 0.0953 (9.53%). The difference increases with larger deformations.