Elongation Calculator
Enter your specimen dimensions to find percent elongation, engineering strain, true strain, and change in length. Switch to the Axial Deformation mode to calculate extension from applied force, cross-section, and Young's modulus. Choose a material preset to instantly compare your result against the typical elongation at break for that material. All results update as you type.
Formula
Worked example
A steel tensile bar has Lo = 50 mm gauge length and fractures at Lf = 60 mm. Change in length: 60 - 50 = 10 mm. Engineering strain: 10 / 50 = 0.200. Percent elongation: 0.200 x 100 = 20.0 %. True strain: ln(60/50) = ln(1.20) = 0.1823. For mild steel (elongation at break ~20 %), the safety ratio is 20.0 / 20 = 1.00, meaning the bar is right at the fracture limit.
What is percent elongation?
Percent elongation (also called elongation or engineering elongation) measures how much a material stretches relative to its original gauge length before it fractures. It is one of the key ductility indicators in materials testing, reported after a standard tensile test such as ASTM E8 (metals) or ISO 6892. A higher percent elongation means a more ductile material that can absorb energy through plastic deformation before breaking. Brittle materials such as glass or hard ceramics have elongations near zero, while soft polymers and annealed metals can exceed several hundred percent.
Engineering strain vs. true strain
Engineering (Cauchy) strain assumes the original gauge length throughout the deformation: it equals change in length divided by original length. True (logarithmic) strain accounts for the continuously shrinking gauge section by taking the natural logarithm of the length ratio (ln(Lf / Lo)). At small strains the two are nearly identical, but they diverge meaningfully above about 5 % elongation. True strain is the physically correct measure for large plastic deformations, and it is additive across successive increments, making it preferred in finite-element models and forming analysis.
Axial deformation and Young's modulus
When the applied force, cross-section, and material stiffness are known, the axial deformation (extension or compression) of a prismatic member is given by the formula delta = F * L / (A * E), where F is the force in newtons, L the member length in mm, A the cross-sectional area in mm^2, and E the Young's modulus in GPa (multiplied internally by 1000 to convert to N/mm^2). This is the linear-elastic (Hookean) result and applies only in the elastic region, before the material yields. Switching to Axial Deformation mode in this calculator lets you solve for the deformation given those three inputs, then automatically converts it to percent elongation and strain.
How to use the elongation at break comparison
Every material has a characteristic elongation at break: the maximum percent elongation measured at the fracture point in a standard test. Selecting a material preset loads that value, and the calculator divides your computed elongation by it to produce a safety ratio. A ratio below 0.5 is generally safe (you are in the moderate deformation range), 0.5-0.8 is moderate, 0.8-1.0 is close to the fracture threshold, and 1.0 or above means the specimen would be expected to break. This comparison is useful for quickly assessing whether a proposed strain is feasible for the chosen material or whether a tougher, more ductile alternative is needed.
Typical elongation at break for common engineering materials
| Material | Elongation at break (%) | Young's modulus (GPa) | Category |
|---|---|---|---|
| Mild Steel | 20 | 200 | Metal |
| Stainless Steel 304 | 40 | 193 | Metal |
| Aluminum 6061-T6 | 12 | 68.9 | Metal |
| Copper (annealed) | 60 | 110 | Metal |
| Brass 70/30 | 68 | 100 | Metal |
| Titanium Grade 2 | 20 | 105 | Metal |
| ABS | 5 | 2.3 | Polymer |
| Nylon 6/6 | 60 | 3.0 | Polymer |
| PLA | 5 | 3.5 | Polymer |
| TPU | 500 | 0.05 | Polymer |
Values are approximate and depend on alloy grade, heat treatment, and test method (ASTM E8 / ISO 6892).
Frequently asked questions
What is the formula for percent elongation?
Percent elongation = ((Lf - Lo) / Lo) x 100, where Lo is the original gauge length and Lf is the final length at or after fracture. Engineering strain is the same ratio without the multiplication by 100.
What is the difference between elongation and elongation at break?
Elongation is a general term for any extension of a specimen, expressed as a percentage of the original length. Elongation at break (or fracture strain) is the specific elongation measured at the moment the specimen fractures in a tensile test, and it represents the upper ductility limit of the material.
Why is true strain different from engineering strain?
Engineering strain uses the fixed original length as the reference, while true (logarithmic) strain updates the reference length continuously as the specimen deforms. At small strains (under ~5 %) they are nearly equal. At large strains they diverge: a 100 % engineering strain corresponds to a true strain of ln(2) = 0.693, which is the physically correct value for finite deformation analysis.
How does the axial deformation formula work?
The axial deformation (delta) of an elastic bar under a load F is delta = F * L / (A * E). Here L is the member length, A the cross-sectional area, and E the Young's modulus. It assumes the material is linearly elastic and the deformation is small. If the calculated stress (F / A) exceeds the yield strength of the material, the formula no longer applies and plastic analysis is needed.
Which materials have the highest elongation at break?
Elastomers and soft polymers lead the list: natural rubber can reach 700 %, TPU (thermoplastic polyurethane) around 500 %, and HDPE up to 700 %. Among metals, annealed copper (about 60 %) and brass (about 68 %) are among the most ductile engineering alloys. Brittle materials such as PLA, glass, or hardened tool steel have elongations well below 5 %.
What units can I use?
In Percent Elongation mode the calculator works in any consistent length unit (mm, cm, m, inches, or feet) because only the ratio matters. In Axial Deformation mode the inputs are fixed: force in newtons, length in millimetres, area in mm^2, and Young's modulus in GPa. The deformation output is in millimetres, and the percent elongation is dimensionless.