text: The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change. Ignoring pressure, one may write:
  where  is some area of interest on the object, and  is the rate of change of that area per unit change in temperature.
  The change in the area can be estimated as:
  This equation works well as long as the area expansion coefficient does not change much over the change in temperature , and the fractional change in area is small . If either of these conditions does not hold, the equation must be integrated.