How to Calculate Elastic Modulus

The elastic modulus, also known as the modulus of elasticity, or Young's modulus, is essentially a measurement of the stiffness of a material. Thus it is commonly used in design and engineering applications. Values used in calculating elastic modulus are generally gathered using data from carefully controlled experiments where forces are imposed on materials. The steps below detail the calculation of elastic modulus using the values from such an experiment and a formula that is derived from Hooke's law, which states that the elastic modulus is equal to the ratio of stress to strain.

Difficulty: Moderately Challenging

Instructions

1. Obtain the numerical values for the following variables from the experiment:
   F = the force applied to the material
   A = the cross-section area through which the force was applied to the material
   L2 = amount the length of the material changes when the force is applied
   L1 = original length of the material (before the force was applied)

2. Substitute the values obtained into the following equation:
   E = (F)(L1)/(A)(L2)
   Where E = Elastic Modulus

3. Multiply the value of F by the value of L1; then divide that quantity by the product of A times L2.

4. The resulting value of these calculations is the elastic modulus of the material.

Tips & Warnings

• Elastic modulus values range from about 1,500 psi (pounds per square inch) for rubber to about 175 million psi for diamond.

References

• Young's Modulus (Elastic Modulus)

Resources

• Properties of Metals and Materials