True Strain Calculator

True strain, also called logarithmic or natural strain, measures deformation against the specimen's continuously changing length. Engineering strain uses the original gauge length as a fixed reference and is calculated as (L − L₀) / L₀. That simple definition works well for small elastic changes, but it becomes less representative when deformation is large. True strain instead accumulates each tiny length increment relative to the current length. Integrating those increments gives εtrue = ln(L/L₀), or equivalently ln(1 + εengineering). The result is dimensionless because it is the logarithm of a length ratio. For a specimen that grows from 100 mm to 110 mm, engineering strain is 0.1 while true strain is approximately 0.09531. The values are close because the deformation is modest. At 50 percent engineering strain, however, true strain is about 0.40547 rather than 0.5. In compression, both values are negative, and the logarithmic expression remains valid as long as the final length and the ratio 1 + engineering strain stay positive. A value of -1 engineering strain would imply zero final length and is therefore outside the formula's physical domain. Logarithmic strain is useful in tensile testing, metal forming, rolling, drawing, extrusion, and simulations involving substantial shape change. Its additive property is especially valuable: true strains from sequential deformation steps can be added, whereas engineering strains generally cannot. Under the common idealization of constant volume during plastic flow, cross-sectional area varies inversely with the length ratio. This calculator uses that assumption to estimate final area when an initial area is supplied. It also converts engineering stress to true stress with σtrue = σengineering(1 + εengineering), an approximation valid before localized necking. Use consistent units for initial and final length; millimetres, inches, or metres all produce the same strain when both entries share a unit. Stress retains whatever unit you enter, and calculated area retains the initial area's unit. Real materials may not conserve volume, and after necking begins the uniform-area conversion no longer describes local behavior accurately. Measurements of instantaneous diameter or area are preferable in that regime. The outputs support education and preliminary analysis, but material qualification and safety-critical design should rely on applicable test standards, calibrated measurements, and a complete constitutive model.