Strain percentage:
extension as a share of the original length

Strain as a pure ratio

Stretch a rubber band by 2 cm and it feels like a lot. Stretch a bridge cable by 2 cm and engineers barely notice. The raw extension is not very informative until you compare it with the length the stretching happened over, and that comparison is called strain.

Because it divides one length by another, strain has no unit. A strain of 0.004 means the object has lengthened by 0.4 percent of its original length, whether the measurement was taken in millimetres, inches or kilometres.

Strain pairs with stress. Stress is the load per area acting on the material; strain is how much the material deforms in response. Plot one against the other and you get the stress-strain curve that describes a material's behaviour.

Formula and sign conventions

Both lengths must be in the same unit. A sample of 500 mm that extends by 0.2 cm has ΔL of 2 mm, and mixing the units gives a wrong answer by a factor of ten.

Strain is sometimes quoted in microstrain (με), meaning millionths. A strain of 0.004 is 4,000 με. Strain gauges on structures typically report values of tens to hundreds of microstrain, because steel in service strains very little.

Worked example: a 500 mm bar that gains 2 mm

A metal bar is 500 mm long before loading. Under tension its length measured between the same two marks becomes 502 mm.

If the bar were 5 m long and extended by 20 mm under the same strain, ΔL ÷ L₀ would be 20 ÷ 5,000 = 0.004 again. The strain is a property of the stretching state, independent of the sample's size, which is why material tests use standard specimens and scale results.

In reverse, you can predict extension from strain: a 1.2 m member strained to 0.0005 lengthens by 1,200 × 0.0005 = 0.6 mm.

What strain levels look like for different materials

Metals in normal use operate at strains far below one percent, which is why small movements need precise instruments. If your calculation shows 5 percent elastic strain in steel, a unit or reading error is more likely than a real result.

Beyond the elastic limit, the material does not return to its original length when unloaded. That permanent change is plastic strain, and the simple linear relationship between stress and strain no longer applies.

Strain compared with ordinary percentage change

Strain percentage is the same calculation as a percentage change in length: (new − old) ÷ old × 100. That makes a generic percentage-change tool a valid cross-check. The difference is conceptual rather than numerical, since in mechanics the reference length is always the original, unloaded one.

• Reference length: always the starting length, not the final one. Dividing 2 by 502 gives 0.398%, a small but real mistake.
• Gauge length: measure between the same two marks before and after, not over the whole specimen.
• Direction: lateral shrinking is also strain, usually negative; the ratio of lateral to axial strain is Poisson's ratio.

From stress to strain, and strain from heat

Inside the elastic range, strain follows from stress through the modulus: ε = σ ÷ E. A steel member under 100 MPa, with E = 200,000 MPa, has a strain of 0.0005, which is 0.05 percent. Pulling a rod lengthwise also thins it; with a Poisson's ratio of 0.3 the sideways strain is about −0.00015.

Temperature changes cause strain as well, even with no load. Thermal strain equals the expansion coefficient times the temperature rise. A 10 m steel rail (about 12 × 10⁻⁶ per kelvin) warmed by 30 K grows 10,000 × 12 × 10⁻⁶ × 30 = 3.6 mm, whereas the same length of aluminium (about 23 × 10⁻⁶ per kelvin) grows 6.9 mm.

If the ends are restrained, that blocked growth turns into stress instead of movement, which is why bridges have expansion joints and railways leave gaps or use stress-free temperature settings.

Reading strain in test reports

Material data sheets quote 'elongation at break' as a percentage over a gauge length, commonly 50 mm or five times the diameter. A mild steel with 25 percent elongation means that a 50 mm gauge length stretched to 62.5 mm before fracture.

Short gauge lengths give higher percentages because most of the stretch is concentrated at the neck, so compare elongations only when the gauge lengths match.

When a design limit is expressed as strain, such as 0.2 percent proof strain, divide by 100 to use it in the formula. A 0.2 percent proof strain on a 500 mm bar is a permanent offset of 1 mm.

Good habits when measuring strain

Mark the gauge length with a fine scribe or use an extensometer rather than eyeballing a ruler across a bent specimen. Keep the specimen aligned with the load so that the extension is axial and not partly bending.

Take readings at several load steps. A plot of strain against load should be a straight line in the elastic range; a curve or scatter hints at slipping grips, a loose clamp or yielding.

Record the temperature as well. Thermal expansion causes strain without any load: steel grows by about 12 millionths per kelvin, so a 20-degree warm-up in a 500 mm bar gives roughly 0.12 mm of free extension.