True Strain Calculator

True strain: A logarithmic strain measure based on the current length change during deformation. It is often called logarithmic strain.

Engineering strain: Change in length divided by the original length. This is the simpler strain measure many tensile-test reports start with.

Stretch ratio: The current length divided by the original length. A value above 1 means elongation, and below 1 means shortening.

True stress: Stress converted from engineering stress with the common pre-necking relation used for uniform uniaxial deformation.

Engineering stress: Nominal stress based on the original cross-sectional area, not the current area.

Difference from engineering strain: The signed percent difference between true strain and engineering strain, using engineering strain magnitude as the reference when possible.

Assumption note: A short reminder about when the true-stress conversion is appropriate and when caution is needed.

Mistake: Entering 10 instead of 0.10 in Engineering strain (decimal) .
Fix: Enter strain as a decimal. For 10%, use 0.10 so True strain and Difference from engineering strain are correct.

Mistake: Using different units for Initial length (selected unit) and Final length (selected unit) .
Fix: Keep both lengths in the same Length unit before calculating Stretch ratio and True strain .

Mistake: Entering 0 or a negative value for Initial length (selected unit) or Final length (selected unit) .
Fix: Use values greater than 0. The logarithm for True strain needs a positive length ratio.

Mistake: Turning on Also convert engineering stress to true stress but leaving Engineering stress (MPa) blank.
Fix: Enter a valid stress value and make sure Stress unit matches what you typed so True stress uses the right unit.

Mistake: Using True stress after necking as if the simple conversion always stays valid.
Fix: Read the Assumption note . The reported True stress is mainly for uniform deformation before necking.

Mistake: Thinking a negative True strain means the calculator failed.
Fix: Negative True strain is normal for shortening or compression. Check whether your Final length (selected unit) is smaller than your initial length.

• The true-strain formulas here are for uniaxial deformation and require a positive length ratio.
• Engineering strain (decimal) must be greater than -1 because ln(1 + e) is undefined at -1 or below.
• The simple True stress conversion assumes roughly uniform deformation before necking; after necking, local area change is no longer uniform, so the result can differ from measured true stress.
• The calculator does not estimate changing cross-sectional area directly; it uses the standard conversion from engineering stress and engineering strain.
• If Engineering strain is exactly 0, the percent comparison is reported as 0 to avoid division by zero.
• Length unit affects display consistency only. The strain results are unitless as long as both lengths use the same unit.
• Output formatting can change how many digits you see, but it does not change the underlying calculation.

Core equations

The calculator first determines engineering strain from the selected input mode, then converts it to true strain. True strain is the natural-log form commonly used for finite deformation [1][2].

e = (L - L0) / L0

ε_true = ln(L / L0)

ε_true = ln(1 + e)

λ (stretch ratio) = L / L0 = 1 + e

Stress conversion

If stress conversion is turned on, the calculator converts the entered engineering stress to true stress with the standard pre-necking relation for uniform uniaxial deformation [1].

σ_true = σ_eng x (1 + e)

Stress-unit display uses exact unit conversions where applicable, including 1 GPa = 1000 MPa, 1 MPa = 1000000 Pa, 1 ksi = 6.894757 MPa, and 1 psi = 6894.757 Pa.

Difference from engineering strain

To show when finite-deformation effects matter, the calculator reports the signed percent difference between true strain and engineering strain. A negative value means true strain is smaller than engineering strain; a positive value means it is larger.

diff_pct = 100 x (ε_true - e) / abs(e)

If engineering strain is exactly 0 and true strain is also 0, the difference is reported as 0. This avoids division by zero.

Worked example

Suppose L0 = 50 mm and L = 55 mm. Then engineering strain is (55 - 50) / 50 = 0.10. True strain is ln(55 / 50) = ln(1.1) = 0.0953101798. The stretch ratio is 55 / 50 = 1.1. The percent difference from engineering strain is 100 x (0.0953101798 - 0.10) / 0.10 = -4.6898202%. If engineering stress is 250 MPa, then true stress is 250 x 1.1 = 275 MPa.

Validation and mode rules

In lengths mode, the calculator uses Initial length (selected unit) and Final length (selected unit) and ignores the hidden engineering-strain field. In engineering-strain mode, it uses Engineering strain (decimal) and ignores the hidden length fields. If stress conversion is off, the hidden stress field is not used.

Practical assumptions behind the results

The strain conversion is mathematically exact for the entered length ratio, but the simple true-stress conversion is mainly a pre-necking approximation under uniform deformation. Real test data can differ after necking, with nonuniform strain, or when local area change is measured directly instead of inferred.