Tension specimen
Given: L₀ = 100 mm, ΔL = 0.20 mm
Working: ε = 0.20 / 100 = 0.002
Strain = 0.002 = 0.2% = 2000 µε.
Materials Engineering
Strain Formula
Learn the engineering strain formula ε = ΔL/L₀, convert strain to percent and microstrain, and calculate elongation ratio with worked examples.
Governing equation
ε = ΔL / L₀ = (L − L₀) / L₀
Engineering strain measures deformation relative to an original gauge length. Because it is a ratio of two lengths, strain itself is dimensionless.
Engineering strain uses the original length L₀ as the reference. For large deformations, true strain may be more appropriate depending on the analysis.
Live calculator
Engineering strain calculator
Uses ε = ΔL/L₀ with both lengths in the same unit.
Result
0.002strain
0.2% = 2,000 µε
Formula variables and units
| Symbol | Meaning | Typical SI unit |
|---|---|---|
| ε | Engineering strain | dimensionless |
| ΔL | Change in length | same length unit as L₀ |
| L₀ | Original gauge length | mm, m, etc. |
| L | Final length | same as L₀ |
How to calculate it
- 1Measure the original gauge length.
- 2Measure the change in length under the condition of interest.
- 3Use the same units for ΔL and L₀.
- 4Divide ΔL by L₀.
- 5Multiply by 100 for percent strain or by 1,000,000 for microstrain.
Common mistakes
- Using different units for extension and original length.
- Reporting 0.002 as 0.002% instead of 0.2%.
- Dropping the sign convention for tension/compression without stating it.
- Confusing engineering strain with stress.
Worked examples
Compression sign
Given: A member shortens by 0.10 mm over 50 mm
Working: ε = -0.10 / 50
Engineering strain = -0.002, where the negative sign denotes shortening under the chosen convention.
Go deeper
Use the dedicated OneCalcApp tool
The quick calculator above demonstrates the governing equation. Open the related engineering tool for broader inputs, outputs and calculation context where available.
Frequently asked questions
What is the strain formula?
Engineering strain is ε = ΔL/L₀, where ΔL is the change in length and L₀ is the original length.
Does strain have a unit?
Strain is dimensionless because it is a ratio of two lengths, but it is often expressed as percent strain or microstrain.
How do I convert strain to microstrain?
Multiply the dimensionless strain value by 1,000,000.
What is the difference between stress and strain?
Stress is force per area, while strain is relative deformation.
Related formula guides
Continue with another problem-first engineering equation.