Strain formula
Strain measures how much a material stretches or compresses relative to its original length. It is the deformation side of the stress-strain relationship, and it is dimensionless, often quoted as a percentage.
Variables
| ε | Strain (dimensionless) | in/in or m/m |
| ΔL | Change in length | in or m |
| L | Original length | in or m |
Rearranged
L = ΔL / ε
Worked example
A 2 m steel bar stretches by 1 mm under load.
Divide the change by the original length: 0.001 / 2 = 0.0005.
Strain has no units because it is a length divided by a length. For elastic materials it links to stress through the modulus of elasticity by Hooke law, stress equals modulus times strain, so a small strain in stiff steel still represents a large stress.
Relating strain to stress?
Use the Modulus of Elasticity Table to convert strain into stress with Hooke law.
Elastic and plastic strain
Up to the yield point, strain is elastic: remove the load and the material springs back to its original length. Beyond yield it becomes partly plastic, leaving a permanent set. Design normally keeps parts in the elastic range, where strain and stress stay proportional and predictable.
Engineering vs true strain
Engineering strain uses the original length as the reference, which is convenient and accurate for the small strains of most structural work. True strain references the instantaneous length and matters in metal forming, where large deformations make the difference between the two definitions significant.
FAQ
What is the formula for strain?
Strain equals the change in length divided by the original length, epsilon = delta L over L. It is dimensionless.
Does strain have units?
No. It is a ratio of two lengths, so it is unitless, though it is often expressed as a percentage or in microstrain.
How is strain related to stress?
In the elastic range they are proportional through Hooke law: stress equals the modulus of elasticity times strain.