Enter values to see results
—
—
%
—
με
—
mm
Enter values to see results
—
—
%
—
με
—
mm
The Strain Calculator determines the engineering strain experienced by a material under deformation. Strain is a dimensionless quantity that measures the relative change in length of a body and is one of the most fundamental concepts in solid mechanics and materials science.
Engineering strain is defined as:
$$\varepsilon = \frac{\Delta L}{L_0}$$
where $$\Delta L$$ is the change in length and $$L_0$$ is the original gauge length. Alternatively, when stress and the elastic modulus are known, Hooke's law provides:
$$\varepsilon = \frac{\sigma}{E}$$
where $$\sigma$$ is the applied stress in pascals and $$E$$ is Young's modulus. This relationship holds in the linear elastic regime, where deformation is fully reversible. Strain values are often expressed as a decimal, a percentage, or in microstrain ($$1\,\mu\varepsilon = 10^{-6}$$), depending on the application. Strain gauges in structural health monitoring typically read in microstrain, while tensile test data may report percentage elongation.
Understanding strain is essential for predicting material failure, designing load-bearing structures, and interpreting experimental data from mechanical testing. This calculator supports both the geometric (deformation-based) and constitutive (stress-based) approaches.
Strain quantifies deformation without reference to the material's size, making it a universal measure for comparing behavior across different specimens and scales.
From Deformation: When a bar of original length $$L_0$$ is stretched to a new length $$L$$, the elongation is $$\Delta L = L - L_0$$, and the engineering strain is:
$$\varepsilon_{\text{eng}} = \frac{\Delta L}{L_0} = \frac{L - L_0}{L_0}$$
This definition assumes the deformation is referenced to the original undeformed length. For small strains ($$\varepsilon < 0.01$$), engineering strain closely approximates the true (logarithmic) strain.
From Stress via Hooke's Law: Within the elastic limit, stress and strain are proportional:
$$\sigma = E \varepsilon \quad \Rightarrow \quad \varepsilon = \frac{\sigma}{E}$$
Young's modulus $$E$$ is a material property: steel has $$E \approx 200\,\text{GPa}$$, aluminum $$E \approx 70\,\text{GPa}$$, and concrete $$E \approx 30\,\text{GPa}$$.
Unit conversions:
Strain can be tensile (positive, elongation) or compressive (negative, shortening). This calculator reports the absolute magnitude; sign conventions depend on your coordinate system.
The Engineering Strain is the dimensionless ratio of deformation to original length. Values below $$0.002$$ (0.2%) are typically elastic for metals. The Strain Percentage is simply the strain multiplied by 100, commonly used in tensile test reports. Microstrain is the standard unit for strain gauge measurements, where $$1\,\mu\varepsilon = 10^{-6}$$. The Final Length gives the deformed specimen length. If the strain exceeds the yield strain of the material, permanent plastic deformation occurs.
Inputs
Results
A 100 mm steel gauge length elongated by 0.5 mm gives ε = 0.005 (0.5%). This is beyond the elastic limit for most steels (yield strain ~0.1-0.2%), indicating plastic deformation.
Inputs
Results
An applied stress of 140 MPa on aluminum (E = 70 GPa) produces ε = 0.002 (0.2%), near the typical 0.2% offset yield point for 6061-T6 aluminum.
Engineering strain uses the original length as the reference: $$\varepsilon_{\text{eng}} = \Delta L / L_0$$. True (logarithmic) strain uses the instantaneous length: $$\varepsilon_{\text{true}} = \ln(L/L_0)$$. For small deformations they are nearly equal, but they diverge significantly at large strains. True strain is additive for sequential deformations, which makes it preferred in plasticity theory and metal forming analysis.
Microstrain ($$\mu\varepsilon$$) equals $$10^{-6}$$ strain. It is the standard unit for strain gauge measurements because most structural strains are very small. For example, a strain of 0.001 equals 1000 $$\mu\varepsilon$$. Using microstrain avoids awkward decimal notation and makes it easier to compare readings across different sensors and structures.
Hooke's law ($$\sigma = E\varepsilon$$) is valid only in the linear elastic region of the stress-strain curve. Beyond the proportional limit, the relationship becomes nonlinear. Past the yield point, permanent plastic deformation occurs and the material no longer returns to its original shape upon unloading. The elastic limit varies by material: ~0.1% strain for mild steel, ~0.5% for some polymers.
Yes. Compressive loading produces negative strain (shortening), while tensile loading produces positive strain (elongation). Shear strain, defined as the angular distortion $$\gamma = \tan\theta \approx \theta$$ for small angles, can also be positive or negative depending on the direction of shearing.
Yield strain $$\varepsilon_y = \sigma_y / E$$. For mild steel: $$\sigma_y \approx 250\,\text{MPa}$$, $$E = 200\,\text{GPa}$$, so $$\varepsilon_y \approx 0.00125$$ (0.125%). For aluminum 6061-T6: $$\sigma_y \approx 276\,\text{MPa}$$, $$E = 69\,\text{GPa}$$, so $$\varepsilon_y \approx 0.004$$ (0.4%). Titanium Ti-6Al-4V: $$\varepsilon_y \approx 0.008$$ (0.8%).
Strain gauges work on the principle that a conductor's electrical resistance changes when it is stretched or compressed. A thin metallic foil pattern bonded to a surface deforms with the structure, causing a resistance change $$\Delta R / R = G_f \cdot \varepsilon$$, where $$G_f$$ is the gauge factor (typically ~2 for metallic gauges). A Wheatstone bridge circuit converts this tiny resistance change into a measurable voltage signal.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Young's Modulus Calculator
Materials Science & Solid Mechanics
Shear Modulus Calculator
Materials Science & Solid Mechanics
Bulk Modulus Calculator
Materials Science & Solid Mechanics
Poisson's Ratio Calculator
Materials Science & Solid Mechanics
Stress Calculator
Materials Science & Solid Mechanics
True Strain Calculator
Materials Science & Solid Mechanics
