Calculation
ε = ΔL / L0
Strain is dimensionless; 0.001 equals 0.1% or 1,000 µm/m.
ε = ΔL/L0
Strain Calculator from Elongation
Strain is dimensionless; 0.001 equals 0.1% or 1,000 µm/m.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Engineering strain ε — The engineering strain – how much the part has stretched or shortened relative to its original length. Dimensionless; often also given in µm/m or percent (0.001 = 1000 µm/m = 0.1%).
- Length change ΔL — The measured length change between the unloaded and loaded state. Source: calliper, dial gauge or a strain gauge. Positive for elongation (tension), negative for shortening (compression).
- Original length L0 — The original or gauge length before the load is applied. Source: calliper or a drawing dimension.
Example
0.1 mm over 100 mm is ε = 0.001 = 0.1%.
Assumptions and limits
Small strain; local plasticity and Poisson contraction are not evaluated.
Understand Strain Calculator from Elongation
This calculator finds the missing quantity among engineering strain ε, elongation ΔL and original length L0 from the other two. It shows why strain is reported as a dimensionless ratio, and puts typical strain values in perspective through the huge gap between stretchy rubber and brittle steel.
What does this quantity describe?
Engineering strain is a loaded part's relative change in length: ε = ΔL/L0. It is dimensionless and is often additionally expressed as a percentage or in µm/m.
Natural rubber can stretch by up to about 700% before breaking, while many steel grades already fracture at around 10-20% elongation — and stay purely elastic only up to a few tenths of a percent. This difference of more than thirtyfold explains why a rubber band stretches easily while a steel wire at a comparable relative elongation would long since have snapped.
Formula and variables
ε = ΔL / L0
ε = ΔL / L0ΔL = ε · L0L0 = ΔL / ε
| Symbol / input | Meaning |
|---|---|
| Engineering strain ε | The engineering strain – how much the part has stretched or shortened relative to its original length. Dimensionless; often also given in µm/m or percent (0.001 = 1000 µm/m = 0.1%). |
| Length change ΔL | The measured length change between the unloaded and loaded state. Source: calliper, dial gauge or a strain gauge. Positive for elongation (tension), negative for shortening (compression). |
| Original length L0 | The original or gauge length before the load is applied. Source: calliper or a drawing dimension. |
Choose the inputs correctly
Enter two of the three quantities. Strain requires elongation and original length, elongation requires strain and original length, original length requires strain and elongation. Measure ΔL and L0 over the same, clearly defined gauge length.
How to use the calculator
Select the target quantity and enter the two known values with units. Check whether a percentage or a plain ratio is expected, and convert with the factor 100 as needed.
Worked example
Given ΔL = 0.1 mm and L0 = 100 mm, substitution gives ε = 0.1/100 = 0.001, or 0.1% (1,000 µm/m).
Understand the result and units
A strain of 0.001 (0.1%) means the part elongated by one thousandth of its original length. For many metallic materials, the purely elastic range, where the part fully returns to shape after unloading, extends only to about 0.1-0.2% strain.
Strain is dimensionless; common forms are the plain ratio (e.g. 0.001), percentage (0.1%), or µm/m / µε (1,000 µm/m equals 0.001).
Typical applications
Strain measurements are used in materials testing (tensile test), evaluating strain-gauge readings on components, deflection control in structural engineering, and quality testing of stretchable materials such as rubber and plastics.
Assumptions, limits and common mistakes
The formula describes engineering (nominal) strain relative to the original length L0. At large deformations, as seen in rubber or ductile metals near fracture, engineering strain increasingly diverges from true (logarithmic) strain, which is referenced to the current instantaneous length.
Common mistake: Do not confuse strain with elongation: ΔL is an absolute length (e.g. in mm), ε is the dimensionless ratio to it. Also, at very large strains (well above a few percent), do not apply the linear approximation ε = ΔL/L0 uncritically, since it doesn't capture Poisson contraction and other nonlinear effects.
Frequently asked questions
Why is strain reported without a unit?
Because it's the ratio of two lengths (ΔL/L0), so the length units cancel. Percentage or µm/m forms are still common for readability.
How much can rubber stretch compared to steel?
Natural rubber reaches up to about 700% elongation before breaking, while many steel grades manage only about 10-20% — a difference of more than thirtyfold.
Is 0.1% strain a lot or a little?
For most structural steels, that already sits near the top of the purely elastic range; for rubber or many plastics, it's a very small, uncritical strain.