Strain in physics is a measure of how much an object deforms relative to its original size when a force is applied to it. It’s calculated as the ratio of the change in length to the original length, making it a dimensionless quantity with no units. If you stretch a 1-meter rubber band by 0.05 meters, its strain is 0.05, or 5%.
The Basic Formula
Strain is one of the simplest ratios in physics. You take the amount an object has been stretched or compressed (its deformation) and divide by the object’s original length. Written out, it looks like this: strain = ΔL / L, where ΔL is the change in length and L is the original length. The Greek letter epsilon (ε) is the standard symbol.
Because you’re dividing a length by a length, strain has no units. It’s sometimes expressed as a pure decimal (0.002), a percentage (0.2%), or in “microstrain,” which is one millionth of a unit of strain. Microstrain is common in engineering because most real-world materials deform by very small amounts under normal loads. A steel beam supporting a floor might experience strain on the order of a few hundred microstrain, far too small to see with your eyes but critically important for structural safety.
Types of Strain
Not all forces pull in the same direction, and strain takes different forms depending on how the force acts on the object.
- Tensile strain occurs when a material is pulled apart, getting longer in the direction of the force. A bungee cord stretching under a jumper’s weight is in tensile strain.
- Compressive strain is the opposite: the material gets shorter because it’s being squeezed. A concrete column supporting a building experiences compressive strain.
- Shear strain happens when a force acts parallel to a surface rather than perpendicular to it. Think of a deck of cards being pushed sideways across the top while the bottom stays fixed. The cards slide relative to each other, and the angle of that deformation is the shear strain.
- Volumetric strain describes a change in the overall volume of an object, typically caused by uniform pressure from all directions, like the pressure deep underwater squeezing a submarine hull.
How Strain Relates to Stress
Strain rarely exists on its own in physics problems. It’s almost always paired with stress, which is the force applied per unit area of the material (measured in pascals). The relationship between stress and strain is what tells you how a material will behave under load.
For most materials under small deformations, stress and strain are directly proportional. This is Hooke’s Law, and the proportionality constant is called Young’s modulus (represented by Y or E). The formula is: stress = Young’s modulus × strain. A material with a high Young’s modulus, like steel, requires a large force to produce even a small strain. A material with a low Young’s modulus, like rubber, deforms easily. Young’s modulus is essentially a number that captures how stiff a material is.
What Happens as Strain Increases
If you keep increasing the force on a material, it passes through a predictable sequence of stages, each visible on a stress-strain curve.
First comes the elastic region, where the material behaves like a spring. Remove the force and it snaps back to its original shape with no permanent change. The boundary of this region is called the elastic limit or proportional limit, the point where the neat straight line on the stress-strain curve starts to bend.
Beyond that is the yield point, where permanent deformation begins. The material won’t fully return to its original shape even after the force is removed. This is a critical threshold in engineering because any structure deformed past its yield point has been permanently altered.
Continue loading and the material eventually reaches its ultimate tensile strength, the absolute maximum stress it can withstand. After this peak, the material begins to “neck,” thinning rapidly at one spot. Shortly after, it fractures. The total elongation at fracture is a measure of ductility, how much a material can deform before breaking. Ductile materials like copper stretch significantly; brittle materials like glass barely deform at all before shattering.
Engineering Strain vs. True Strain
The simple formula (ΔL / L) gives you what’s called engineering strain. It works well for small deformations, but it has a limitation: it always uses the original length as its reference, even as the object changes shape dramatically.
True strain accounts for this by using the natural logarithm of the ratio of instantaneous length to original length. As a material stretches, each tiny increment of deformation is measured against the current length at that moment rather than the starting length. For small strains, the two values are nearly identical. For large deformations, like metal being stamped into a car panel, the difference matters. Computer simulations of forming and crash testing use true stress and true strain because they provide a much more accurate picture of material behavior during extreme deformation.
Poisson’s Ratio: Strain in Other Directions
When you stretch a rubber band lengthwise, it gets thinner in the middle. This isn’t a coincidence. It’s a fundamental property of materials: strain in one direction causes strain in the perpendicular directions too. Poisson’s ratio describes this relationship. It’s the ratio of the lateral (sideways) strain to the axial (lengthwise) strain, and it’s negative because the two strains go in opposite directions. Stretch something longer and it gets narrower; compress it shorter and it bulges wider.
Most common materials have a Poisson’s ratio between 0.2 and 0.5. Rubber is close to 0.5, meaning it barely changes volume when deformed, it just reshapes. Cork is near zero, which is why it works so well as a bottle stopper: pushing it into a bottle doesn’t cause it to expand sideways and jam. A small number of unusual “auxetic” materials actually have a negative Poisson’s ratio, meaning they get wider when stretched rather than thinner.
How Strain Is Measured
You can’t usually measure strain by holding a ruler up to a bridge beam. Instead, engineers use strain gauges, thin metallic foil patterns bonded directly to a surface. The principle is straightforward: when the surface deforms, the foil stretches or compresses along with it, and stretching a wire changes its electrical resistance. By measuring that resistance change, you can calculate the strain precisely.
The key relationship is that the change in resistance divided by the original resistance is proportional to strain, with a proportionality constant called the gauge factor. This factor is determined experimentally for each gauge type and is typically around 2 for common metallic gauges. The resistance changes involved are tiny, so strain gauges are wired into a sensitive circuit called a Wheatstone bridge that can detect very small shifts in resistance. This setup is used everywhere from aerospace testing to bathroom scales.