True Strain Calculator — Logarithmic Strain ε_true = ln(L/L₀)
True strain (logarithmic strain) measures large deformations more accurately than engineering strain by integrating incremental length changes. Enter the original and deformed gauge length, or the engineering strain, to get the true strain and compare both measures.
Input method
mm
mm
ε_true = ln(L / L₀) = ln(1 + ε_eng)
- 1
Length ratio L ÷ L₀
120 ÷ 100 = 1.2 - 2
True strain ε_true = ln(L ÷ L₀)
ln(1.2) = 0.182322Natural logarithm of the length ratio gives the logarithmic (true) strain.
How does this calculator work?
True strain ε_true = ln(L/L₀) = ln(1 + ε_eng). Unlike engineering strain, it integrates incremental length changes and is additive across deformation steps. At small strains both measures agree; at large strains (> 10%), true strain is significantly smaller than engineering strain and is the correct measure for forming and FEA.
Formula
How this is calculated
Engineering strain ε_eng = ΔL / L₀ uses the original length as the reference, which is accurate for small deformations but underestimates the true material stretch at larger deformations. True strain (also called logarithmic or natural strain) sums infinitesimal increments dL/L over the entire deformation path, yielding ε_true = ln(L/L₀). Because of the additive property of logarithms, successive true strains can be added directly — a useful feature in multi-step forming processes — whereas engineering strains cannot.
The two measures agree closely for small strains (below about 5%): at ε_eng = 0.05, ε_true ≈ 0.0488, a difference of only 2.4%. At large strains the gap grows significantly: at 50% engineering strain (ε_eng = 0.5), ε_true = ln(1.5) ≈ 0.405, about 19% less than the engineering value. True strain is the standard in metal forming, polymer processing, and finite-element analyses of large plastic deformation.
Note that compressive deformation gives a negative strain. The formula requires L/L₀ > 0, so the final length must be positive. For area-based measurements, ε_true = ln(A₀/A) (where incompressibility is assumed). This calculator uses the length-based definition.
Frequently asked questions
Use true strain whenever deformations exceed about 5–10%, particularly in metal forming, sheet-metal stamping, polymer stretching, and FEA of large-deformation problems. Engineering strain is sufficient for elastic analysis of structural steel, concrete, and other materials under service loads where strains stay well below 1%.
Yes — that is one of their key advantages. Rolling a bar from 100 mm to 80 mm and then to 60 mm gives total true strain = ln(80/100) + ln(60/80) = ln(60/100), equal to applying the two reductions together. Engineering strains are not additive in the same way.
For a plastically deforming metal assumed to be incompressible, volume is conserved: ε_true_length + ε_true_width + ε_true_thickness = 0. This makes true strains especially convenient in metal-forming analyses, because the sum of the three principal true strains must equal zero.
Also known as
TG we-Calculate Editorial Team. (2026). True Strain Calculator — Logarithmic Strain ε_true = ln(L/L₀) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/true-strain-calculator
TG we-Calculate Editorial Team. "True Strain Calculator — Logarithmic Strain ε_true = ln(L/L₀)." TG we-Calculate. 2026. https://we-calculate.com/calculator/true-strain-calculator.
TG we-Calculate Editorial Team, "True Strain Calculator — Logarithmic Strain ε_true = ln(L/L₀)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/true-strain-calculator
@misc{wecalculate_true_strain_calculator, title = {True Strain Calculator — Logarithmic Strain ε_true = ln(L/L₀)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/true-strain-calculator}}, year = {2026}, note = {TG we-Calculate} }
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