True Strain Calculator
Convert engineering strain and nominal stress into logarithmic strain and true stress, or work backward from true values, using one consistent current-state model.
Inputs
Active sources: Engineering strain and Engineering stress. Editing a paired field makes that field the source for its conversion.
Live results
True strain
0.095310
εₜ = ln(1 + εₑ)
True stress
8.800 MPa
Engineering stress
8.000 MPa
Length change
10.000%
Strain gap
0.004690
Stress difference
0.800 MPa
True strain 0.095310. True stress 8.800 MPa.
Conversion detail
| Quantity | Engineering / nominal | True / logarithmic | Difference | Relationship |
|---|
The stress conversion assumes uniform deformation and approximately constant volume before necking. After localized necking begins, measured instantaneous area is needed for reliable true stress.
How to use the True Strain Calculator
What this calculator does
This calculator converts between engineering strain and true, or logarithmic, strain. When stress is supplied, it also converts between engineering stress and true stress using the same stretch ratio. It is designed for uniaxial tensile or compressive data where the standard pre-necking relationships are appropriate. It does not determine material strength, yield point, fracture strain, Young's modulus, or a post-necking stress curve from force data alone. The underlying distinction between average engineering strain and integrated true strain is summarized in the University of Illinois solid-mechanics guide to strain measures.
When to use it
Use the calculator when converting a tensile-test data point for finite-element material input, checking a hand calculation, comparing nominal and logarithmic deformation at moderate strain, or translating a stress-strain table before the onset of necking. It is also useful for seeing why engineering and true values are nearly equal at small strain but separate progressively as deformation grows.
How to calculate
- The calculator opens with a complete demonstration: engineering strain 0.1, engineering stress 8 MPa, true strain 0.095310, and true stress 8.8 MPa. The example workbook is immediately available through Download Excel.
- Replace either Engineering strain or True strain. The field you edit becomes the active strain source, and the paired value is recalculated. A value of 0.1 means a 10% length increase, not 0.1%.
- Optionally replace Engineering stress or True stress. The edited stress field becomes the active stress source. Both stress values use the selected Stress unit.
- Review True strain first, then the secondary cards and Conversion detail table. The table keeps engineering, true, and difference values together with the equation used.
- Choose Download Excel to export the current canonical values as a validated XLSX workbook. Reset clears the demonstration and all input data; it can disable Download Excel until a complete valid strain is entered again.
Input guide
Engineering strain is a required dimensionless decimal when it is the active strain source. Enter a finite value greater than – 1; 0.1 is a realistic tensile example, while – 0.1 represents 10% engineering compression. Increasing it raises the stretch ratio and, for positive engineering stress, raises true stress. Do not type 10 for 10%; enter 0.1.
True strain is the logarithm of the current-to-original length ratio. It becomes the required source when edited. A realistic example is 0.09531018, corresponding to engineering strain 0.1. Higher true strain produces an exponentially larger stretch ratio. A common mistake is using base-10 logarithms; this calculator uses the natural logarithm.
Engineering stress is optional and may be positive or negative. It is based on original cross-sectional area. For example, 8 MPa at engineering strain 0.1 converts to 8.8 MPa true stress. Do not mix units between the stress number and Stress unit.
True stress is optional and may also be edited as the source. It represents force divided by instantaneous area under the pre-necking conversion assumption. Entering 8.8 MPa with the demonstration strain returns 8 MPa engineering stress. The conversion should not be extended blindly beyond necking; the Abaqus plasticity documentation states the nominal-to-true relationships and their pre-necking limitation.
Stress unit is required whenever a stress is entered. Available choices are Pa, kPa, MPa, GPa, psi, and ksi. Changing the selection converts both displayed stress values while preserving their physical magnitude. For example, 8 MPa becomes about 1,160.302 psi. The accepted number format uses a decimal point; properly grouped thousands such as 1,200.5 are accepted, but decimal-comma input is rejected rather than silently reinterpreted.
Output guide
True strain is the primary exact mathematical conversion, displayed as a dimensionless decimal. True stress and Engineering stress are displayed in the active stress unit and are estimates under the stated area/volume assumption. Length change is engineering strain expressed as a percentage. Strain gap is engineering strain minus true strain; it is zero at zero strain and grows in magnitude as deformation departs from zero. Stress difference is true stress minus engineering stress. The summary pills repeat the current engineering strain, stretch ratio, and unit. In the Conversion detail table, Engineering / nominal and True / logarithmic show the paired values, Difference shows their signed separation, and Relationship states the identity used.
Worked example
With engineering strain εₑ = 0.1, the stretch ratio is 1 + 0.1 = 1.1. True strain is ln(1.1) = 0.09531018, displayed as 0.095310. With engineering stress σₑ = 8 MPa, true stress is 8 × 1.1 = 8.8 MPa. The length change is 10%, the strain gap is 0.1 – 0.09531018 = 0.00468982, and the stress difference is 0.8 MPa. These values match the first-open results and the workbook checkpoints.
Formula and interpretation
σₜ = σₑ(1 + εₑ) | σₑ = σₜ/(1 + εₑ)
Engineering strain measures total length change against the original gauge length. True strain accumulates incremental changes against the continually changing length, which is why the natural logarithm appears. Engineering stress uses original area, while true stress uses instantaneous area. NASA describes how tensile testing produces stress-strain data used to evaluate strength, strain, modulus, and ductility in its overview of mechanical and tensile testing.
Measurement limits and common mistakes
The equations are identities for the strain measures, but the simple stress conversion adds a physical assumption: uniform deformation with approximately constant volume before necking. Once the specimen necks, local area can fall much faster than the average gauge length indicates, so true stress should be based on measured instantaneous area. Real testing also includes compliance, grip seating, slack, and measurement-location effects. NIST discusses these practical complications in its research on strain correction in tensile testing. Other frequent errors are mixing percent with decimal strain, changing a stress unit without converting the numeric value, and treating total true strain as true plastic strain without subtracting the elastic component required by a constitutive model.