True Strain
Convert engineering strain to true strain using ε_true = ln(1 + ε_eng). Calculate true stress from engineering stress with charts for materials science.
About This Calculator
The True Strain Calculator converts engineering (nominal) strain to true strain and engineering stress to true stress using the standard logarithmic relationship. Engineers, material scientists, and students use this tool to transform experimental tensile test data into true stress-strain curves required for finite element analysis (FEA), structural design, and material characterization.
The calculator applies two fundamental formulas from continuum mechanics. First, true strain is calculated from engineering strain using εtrue = ln(1 + εeng). This logarithmic relationship accounts for the continuous change in specimen length during deformation, providing a more physically accurate strain measure than engineering strain, especially beyond the yield point. Second, if an engineering stress value is provided, true stress is calculated using σtrue = σeng × (1 + εeng), which accounts for the reduction in cross-sectional area under tension.
For small deformations (strain below 5%), the difference between engineering and true strain is negligible — less than 2.5%. However, as materials undergo plastic deformation and necking, the divergence becomes significant. Most commercial FEA software packages including ABAQUS and ANSYS require true stress-strain input to accurately model strain hardening, failure, and large-deformation behavior.
Regional notes: The true strain formula is universally applied in engineering across all regions. Strain is a dimensionless quantity independent of measurement system. Stress values can be entered in any unit — the calculator performs the logarithmic transformation without unit conversion, so the output stress uses the same unit as the input. Common units include MPa (SI), psi or ksi (US customary), and N/mm² (equivalent to MPa).
Frequently Asked Questions
What is true strain?
True strain (ε_true) measures the instantaneous deformation of a material based on its current length rather than the original length. It is calculated using the formula ε_true = ln(1 + ε_eng), where ε_eng is the engineering or nominal strain. Unlike engineering strain, true strain accounts for the changing cross-sectional area during deformation and provides a more accurate representation of material behavior beyond the yield point.
How do I calculate true strain from engineering strain?
To calculate true strain from engineering strain, use the formula ε_true = ln(1 + ε_eng). First add 1 to the engineering strain value, then take the natural logarithm of the result. For example, if the engineering strain is 0.1, the true strain is ln(1.1) = 0.0953. The true strain is always slightly lower than the engineering strain for tensile deformation.
What is the difference between true stress and engineering stress?
Engineering stress uses the original undeformed cross-sectional area of the specimen (σ_eng = Force / A_original), while true stress uses the instantaneous or deformed cross-sectional area (σ_true = Force / A_instantaneous). True stress is always higher than engineering stress in tension because the cross-sectional area decreases as the material stretches. The conversion formula is σ_true = σ_eng × (1 + ε_eng).
Why is true strain important in materials science?
True strain is essential in materials science because it accurately describes material behavior during plastic deformation, especially strain hardening. Engineering stress-strain data is based on the original cross-sectional area, which becomes inaccurate after necking begins. Most CAE and FEA software like ABAQUS and ANSYS require true stress-strain data to correctly model plastic material behavior in simulations.
Can true strain be negative?
Yes, true strain can be negative when a material is under compression. For compressive deformation, the engineering strain is negative (since the length decreases), and the true strain ln(1 + ε_eng) will also be negative. The engineering strain must always be greater than −1 for the natural logarithm to be defined, as ln(0) = −∞ and ln of a negative number is undefined.
What is the relationship between true strain and engineering strain?
True strain (ε_true) and engineering strain (ε_eng) are related by the formula ε_true = ln(1 + ε_eng). For small strains (below 0.1 or 10%), the difference between true and engineering strain is minimal. For example, at ε_eng = 0.05, ε_true = 0.0488 — a difference of about 2.4%. At larger strains, the divergence becomes significant, making the conversion critical for accurate material modeling.
What is the limit of engineering strain in the true strain formula?
The engineering strain must be greater than −1 for the true strain formula ε_true = ln(1 + ε_eng) to be mathematically valid. At ε_eng = −1, the material would be compressed to zero length, giving ln(0) = −∞. For any engineering strain less than or equal to −1, the natural logarithm is undefined or results in an infinite value, which has no physical meaning.
Where is the true strain calculator used in industry?
The true strain calculator is widely used in mechanical engineering, aerospace engineering, civil engineering, and materials science. Engineers use it to convert experimental stress-strain test data from universal testing machines into true stress-strain curves for finite element analysis (FEA), structural design, failure analysis, and quality control of metals, polymers, and composites.