1An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:
λ = stressstrain
where lambda (λ) is the elastic modulus; stress is the force causing the deformation divided by the area to which the force is applied; and strain is the ratio of the change caused by the stress to the original state of the object. If stress is measured in pascals, since strain is a unitless ratio, then the units of λ are pascals as well.
Since the denominator becomes unity if length is doubled, the elastic modulus becomes the stress needed to cause a sample of the material to double in length. While this endpoint is not realistic because most materials will fail before reaching it, it is practical, in that small fractions of the defining load will operate in exactly the same ratio. Thus for steel with an elastic modulus of 30 million pounds per square inch, a 30 thousand psi load will elongate a 1 inch bar by one-thousandths of an inch, and similarly for metric units, where a thousandth of the modulus in Gigapascals will change a meter by a millimeter.
source : wikipedia