Strain & Deformation Calculator — Engineering, True & Axial Strain
Calculate engineering and true strain, length change, and linear-elastic axial deformation from measured lengths, strain, axial stress, or axial force.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Length change
Initial and final length
Strain input
Axial stress and length
Material
Axial load
Geometry
Material
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Engineering strain from length change:
εeng = ΔL / L0
εeng = (Lf − L0) / L0
ΔL = Lf − L0
λ = Lf / L0 = 1 + εeng
True (logarithmic) strain:
εtrue = ln(Lf / L0)
εtrue = ln(1 + εeng)
εeng = eεtrue − 1
Strain to length change:
ΔL = εeng · L0
Lf = L0 + ΔL = L0(1 + εeng)
Axial stress to linear-elastic strain and deformation:
εeng = σ / E
ΔL = (σ / E) · L
Axial force to linear-elastic deformation:
σ = F / A
εeng = F / (A · E)
ΔL = F · L / (A · E)
U = 1/2 · F · ΔL
Alternative strain representations returned by the calculator:
ε [%] = 100 · εeng
ε [µε] = 106 · εeng
where:
- εeng — engineering axial strain, dimensionless
- εtrue — true or logarithmic strain, dimensionless
- ΔL — signed length change; positive for elongation and negative for shortening
- L0 — original length
- Lf — final length
- λ — stretch ratio, dimensionless
- σ — axial normal stress
- E — Young’s modulus
- F — signed axial force; positive in tension and negative in compression
- A — cross-sectional area
- L — original member length used by the elastic calculation
- U — elastic strain energy calculated in axial-force mode
True strain and stretch ratio are calculated in the geometric length/strain modes. The stress and axial-force modes use the one-dimensional linear-elastic relation ε = σ / E and return engineering strain.
When to use this calculator
Use this calculator for one-dimensional axial strain and length-change calculations, from direct geometric measurements or from a linear-elastic axial load model.
- Calculate engineering strain and true strain from an original length and a measured length change.
- Calculate engineering strain, true strain, and stretch ratio from initial and final lengths.
- Convert a known engineering strain or true strain into axial length change for a specified original length.
- Calculate linear-elastic engineering strain and deformation from axial stress, member length, and Young’s modulus.
- Calculate axial stress, engineering strain, deformation, and elastic strain energy from axial force, length, cross-sectional area, and Young’s modulus.
- Express engineering strain as a decimal, percentage, or microstrain for comparison with measurements or engineering data.
The geometric length/strain modes describe deformation without assuming a material model. The stress and axial-force modes should be used only when a one-dimensional linear-elastic approximation is appropriate.
Do not use this calculator as a complete strength or safety check. It does not evaluate yielding, plastic deformation, fatigue, stress concentrations, thermal strain, bending, torsion, multiaxial stress states, or Poisson effects. Compression members also require a separate stability or buckling check where applicable.
How to interpret the result
Engineering strain ε represents the signed change in length divided by the original length. A positive result represents elongation or tensile response, a negative result represents shortening or compressive response, and zero represents no axial length change.
ΔL is the corresponding signed change in length. Its displayed unit follows the selected length unit.
For the geometric length and strain modes:
- Engineering strain is calculated relative to the original length.
- True strain is calculated as ln(Lf / L0).
- The stretch ratio λ is Lf / L0. A value above 1 indicates elongation, a value below 1 indicates shortening, and λ = 1 indicates no length change.
- Engineering strain is also reported as percent strain and microstrain.
Engineering strain and true strain approach the same value as deformation becomes small, but they are different strain measures and diverge as the magnitude of deformation increases.
For the stress mode:
The calculator applies ε = σ / E and ΔL = εL. For a fixed Young’s modulus, increasing the magnitude of axial stress increases the magnitude of strain and deformation. Increasing Young’s modulus decreases both strain and deformation for the same stress.
For the axial-force mode:
The calculator first evaluates σ = F / A and then ε = σ / E and ΔL = εL. For a given material and geometry, deformation increases with axial force and member length, and decreases with cross-sectional area and Young’s modulus.
Axial-force mode also returns U = 1/2 FΔL as the elastic strain energy of the linear-elastic axial model.
- Info — all valid calculations are informational results; the calculator does not apply a safe, warning, or unsafe strain threshold.
- Invalid — returned when required inputs are missing, non-finite, non-positive where a positive value is required, or when the resulting final length would not remain positive.
A valid result does not establish that a component is safe. In the elastic modes, verify that the selected Young’s modulus and the linear-elastic assumption are appropriate. Yielding, local stress concentrations, fatigue, thermal effects, geometric nonlinearity, and other failure modes are not evaluated. Compression results do not verify buckling resistance.
Calculation example
A straight prismatic member carries a tensile axial force of 30 kN. The member is 1.5 m long, has a cross-sectional area of 300 mm², and Young’s modulus is 200 GPa. Calculate the axial stress, engineering strain, elongation, and elastic strain energy.
Input data:
- Mode: Axial force → elastic deformation
- F = 30 kN = 30,000 N
- L = 1.5 m = 1,500 mm
- A = 300 mm²
- E = 200 GPa = 200,000 MPa
Step 1 — Calculate axial stress:
σ = F / A
σ = 30,000 N / 300 mm² = 100 N/mm² = 100 MPa
Step 2 — Calculate engineering strain:
ε = σ / E
ε = 100 MPa / 200,000 MPa = 0.0005
ε = 0.05% = 500 µε
Step 3 — Calculate axial elongation:
ΔL = ε · L
ΔL = 0.0005 · 1,500 mm = 0.75 mm
Step 4 — Calculate elastic strain energy:
ΔL = 0.75 mm = 0.00075 m
U = 1/2 · F · ΔL
U = 1/2 · 30,000 N · 0.00075 m = 11.25 J
Result:
- Axial stress: σ = 100 MPa
- Engineering strain: ε = 0.0005
- Percent strain: 0.05%
- Microstrain: 500 µε
- Axial deformation: ΔL = 0.75 mm
- Elastic strain energy: U = 11.25 J
The positive strain and positive length change indicate tension and elongation. These results are valid only for the calculator’s uniform, linear-elastic axial model. The calculation does not determine whether 100 MPa is acceptable for the selected material and does not check yielding, stress concentrations, fatigue, or other failure modes.
Assumptions and limitations
- The calculator evaluates one-dimensional axial strain and deformation.
- The length-change, initial/final-length, and strain-input modes are geometric conversions only; they do not assume or evaluate material behavior.
- Original length must be greater than zero, and every calculated or entered final length must remain greater than zero.
- Engineering strain entered directly must be greater than −1 because ε = −1 would imply zero final length.
- True strain is converted to engineering strain using εeng = eεtrue − 1 within the supported numerical range.
- The stress mode assumes a uniaxial linear-elastic relation ε = σ / E with constant positive Young’s modulus.
- The axial-force mode assumes a straight prismatic member with constant cross-sectional area and Young’s modulus along its length.
- Axial force is treated as a centered axial load producing uniform normal stress σ = F / A.
- The stress and axial-force modes assume linear-elastic material response and do not model yielding, plasticity, nonlinear stress-strain behavior, or geometric nonlinearity.
- Stress concentrations, holes, notches, joints, local contact effects, residual stresses, creep, viscoelasticity, fatigue, and fracture are not included.
- Thermal strain and thermal expansion are not included.
- Bending, torsion, transverse shear deformation, multiaxial stress states, lateral strain, and Poisson-ratio effects are not calculated.
- Buckling and other stability modes are not checked for members in compression.
- A material selection may provide Young’s modulus automatically, but the user must verify that the selected modulus is appropriate for the actual material, temperature, condition, and application.