What is the unit of strain?

Short Answer:

The unit of strain is dimensionless, meaning it has no unit. Strain is defined as the ratio of change in length to the original length of a material when it is subjected to stress. Since both the numerator and denominator are lengths, their units cancel each other out. Therefore, strain is a pure number and often expressed in decimal or percentage form (%).

In practical use, strain values are very small, so they are sometimes written in microstrain (µε), where 1 µε = 10⁻⁶ strain. It shows very small deformations in engineering materials under load.

Detailed Explanation :

Unit of Strain

Strain is a basic concept in the study of Mechanics of Materials and represents the deformation or change in shape of a body when subjected to stress. When an external force acts on a material, it either elongates, shortens, or distorts depending on the nature of the applied force. The amount of this deformation compared to the original dimension is called strain.

Mathematically, strain (ε) is given as:

where,
ε = Strain,
ΔL = Change in length (in meters),
L = Original length (in meters).

Because both ΔL and L are measured in the same unit (length), they cancel each other out. Hence, strain does not have any physical unit. It is a dimensionless quantity or pure number.

For example, if a bar of 2 meters length is stretched by 0.002 meters, then

This means the strain is 0.001, which can also be written as 0.1% strain.

Expression of Strain in Different Forms

Though strain has no unit, in engineering practice, it is often represented in different convenient forms depending on the magnitude of deformation:

  1. Plain (Decimal) Form:
    Strain can be written directly as a decimal, for example, 0.0005.
  2. Percentage Form:
    To make small values easier to read, strain is expressed as a percentage by multiplying by 100.

For example, if ε = 0.0005, then percentage strain = 0.05%.

  1. Microstrain (µε):
    When the strain values are extremely small (as in metals or structural components), it is expressed in microstrain.

So, 0.0005 strain = 500 µε.

Dimensional Formula of Strain

Since strain is the ratio of two similar quantities (change in length and original length), its dimensional formula is [M⁰ L⁰ T⁰]. This confirms that strain has no dimension and no physical unit. It only represents the relative deformation of a material.

Types of Strain

Even though the unit of strain remains the same for all cases (dimensionless), strain can be classified into different types depending on the nature of deformation:

  1. Tensile Strain:
    It occurs when the material is stretched by a tensile force. The material increases in length.
  2. Compressive Strain:
    It occurs when the material is compressed or shortened due to a compressive load. The material decreases in length.
  3. Shear Strain:
    It occurs when a tangential or shear force acts on a material, causing an angular deformation. Shear strain is measured as the angle of deformation (in radians), but it is also dimensionless because radians are unitless.
  4. Volumetric Strain:
    It represents the ratio of change in volume to the original volume when the material is subjected to uniform pressure in all directions. Like other strains, it also has no unit.

Practical Importance of Strain Measurement

Even though strain is unitless, measuring it accurately is extremely important in engineering applications. Small changes in strain can lead to significant stresses in materials, affecting their safety and performance. Strain measurement helps in:

  • Determining the elastic limit of materials.
  • Calculating stress using Hooke’s Law (σ = Eε).
  • Understanding material behavior under different loading conditions.
  • Designing structures that can safely withstand expected loads.

In laboratories and industries, strain gauges are used to measure minute changes in strain. These gauges convert physical deformation into electrical signals, which can be easily read and analyzed.

Relation Between Stress, Strain, and Elasticity

Stress and strain are directly related by Hooke’s Law, which states that within the elastic limit, stress is directly proportional to strain.

Here, E is the Young’s Modulus of the material, which defines the stiffness.

  • If E is large, the material is stiffer (less strain for the same stress).
  • If E is small, the material is more flexible (more strain for the same stress).

Since strain has no unit, the unit of stress and the modulus of elasticity are the same (N/m² or Pascal).

Example:

Suppose a steel wire 1 m long is stretched by 0.0002 m under a certain load.

Thus, strain = 0.0002 or 0.02% or 200 µε.
This means the wire elongates by only a small fraction of its length, showing the tiny amount of deformation experienced under load.

Engineering Perspective:

Even though strain values are very small, they are crucial for evaluating the performance and safety of structures, bridges, machines, and materials. By understanding strain, engineers can prevent material failure and design systems that work efficiently under applied forces.

Conclusion:

The unit of strain is dimensionless because it is a ratio of two similar quantities—change in length and original length. It has no unit and no dimension. However, in practice, strain is often expressed in decimal, percentage, or microstrain forms for convenience. Although unitless, strain plays a vital role in mechanical design and analysis, helping engineers determine material deformation, elasticity, and structural strength.