Strain Formula
Calculate engineering strain using ε = ΔL/L₀.
Understand how materials deform under load with this fundamental mechanics formula.
The Formula
ε = ΔL / L₀
Strain measures how much a material deforms relative to its original length.
It is a dimensionless ratio — it has no units.
Strain is often expressed as a decimal or a percentage.
Variables
| Symbol | Meaning |
|---|---|
| ε | Strain (dimensionless) |
| ΔL | Change in length (metres, m) |
| L₀ | Original length (metres, m) |
Example 1
A 2-metre steel bar stretches by 0.004 m under load. What is the strain?
ε = ΔL / L₀
ε = 0.004 m / 2 m
ε = 0.002 (or 0.2%)
Example 2
A 500 mm aluminium rod compresses by 0.15 mm. Find the strain.
ε = ΔL / L₀
ε = 0.15 mm / 500 mm
ε = 0.0003 (or 0.03%)
When to Use It
Use the strain formula when you need to:
- Quantify how much a material has deformed under load
- Compare deformation across materials of different lengths
- Calculate Young's modulus when combined with stress data
- Assess whether a material is within its elastic limit
Strain can be tensile (stretching) or compressive (shortening).
If the material returns to its original length when the load is removed, it was in the elastic region.
Key Notes
- This formula gives normal (axial) strain — tensile strain is positive (elongation), compressive strain is negative (shortening); shear strain γ = Δx/h describes a different deformation mode and uses its own formula
- Strain is often expressed in microstrain (με): 1 με = 1 × 10⁻⁶ — steel yields at roughly 1,000–2,000 με, while rubber can reach strains of 500% (ε = 5) before failure
- Poisson's ratio ν links axial and lateral strain: lateral strain = −ν × axial strain — for steel ν ≈ 0.3, meaning a bar stretched lengthwise also narrows by 30% of its axial strain
- Strain gauges measure tiny resistance changes caused by deformation — they are bonded to the surface and wired into a Wheatstone bridge that converts ε into a voltage signal, accurate to ±1 με in practice