The expansion coefficient (or more specifically, the thermal expansion coefficient) is the quotient that measures the relative change in length or volume that occurs when a solid body or a fluid inside a container changes temperature undergoing thermal expansion.

In general, during a heat transfer, the energy that is stored in intermolecular bonds or between two atoms changes. When the stored energy increases, so does the length of these bonds. Thus, solids normally expand when heated and contract when cooled;[1]​ this response behavior to temperature is expressed by the coefficient of thermal expansion (typically expressed in units of °C):.

In general, as already noted, solids expand when heated and contract when cooled. It is usually assumed that the coefficient of thermal expansion is constant (that is, that its value does not vary with temperature), which implies assuming that there is a linear relationship, of proportionality, between increases in temperature and increases in length. This is not strictly true, although for a large number of applications it is an acceptable approximation.

For solids, the most commonly used expansion coefficient is the linear expansion coefficient α.

For any linear dimension, it can be measured experimentally by comparing the value of said magnitude before and after a certain change in temperature, such as:

The symbol for this coefficient is usually the Greek letter alpha or the letter lambda.

In gases and liquids it is more common to use the volumetric expansion coefficient or , which is given by the expression:.

For solids, volumetric expansion can also be measured, although it is less important in most technical applications. From the calculation it is deduced that the volumetric expansion coefficient is three times the linear expansion coefficient, therefore, for the ranges where the coefficient is constant it is true that:

Knowledge of the linear expansion coefficient acquires great technical importance in many areas of both industrial design and the construction of large structures.

Warning: In this example, a linear expansion coefficient for steel of 1.2 10^-5 is assumed, however the coefficient table indicates another quantity for said material (11.5 10-6 °C-1), keep in mind that the value may not be correct.

Note: The SI unit of temperature is the kelvin (K). However, since increases in temperature are handled in the formula, the use of kelvin or degrees Celsius is equivalent.