True Strain Calculator

What Is a True Strain Calculator?

True strain, also called logarithmic strain, measures deformation relative to the current length of a specimen rather than its original length. It stays accurate through large deformations where engineering strain drifts because the reference length keeps changing. The True Strain Calculator converts initial and final length, or a known engineering strain, into true strain.

How the Calculation Works

Engineering strain uses the original length as its reference, while true strain integrates each small increment of elongation against the current length. The calculator accepts either pair of lengths or a known engineering strain, and reports true strain, engineering strain, and the length ratio together:

$$\varepsilon_{eng} = \frac{L - L_0}{L_0} = \frac{L}{L_0} - 1$$

$$\varepsilon_{true} = \ln\!\left(\frac{L}{L_0}\right) = \ln\!\left(1 + \varepsilon_{eng}\right)$$

Where:

• L₀ is the initial gauge length
• L is the final length after deformation
• ε_eng is the engineering strain
• ε_true is the true (logarithmic) strain, dimensionless

Worked Example

A test coupon stretches from 100 mm to 110 mm. The length ratio is 110/100 = 1.1, so the engineering strain is 0.10 and the true strain is ln(1.1) = 0.09531. True strain is always slightly smaller than engineering strain for tensile elongation, and the gap widens as strain grows.

For related materials tools, see the Young Modulus Calculator and Wire Resistance Calculator.