Enter the final volume and initial volume into the calculator to determine the Expansion Index. This calculator can also evaluate any of the variables given the others are known.

Expansion Index Formula

The following formula is used to calculate the Expansion Index.

EI = (Vf - Vi) / Vi


  • EI is the Expansion Index
  • Vf is the final volume (m³)
  • Vi is the initial volume (m³)

To calculate the Expansion Index, subtract the initial volume from the final volume. Then, divide the result by the initial volume. The result is the Expansion Index, which represents the relative change in volume.

What is an Expansion Index?

An Expansion Index is a measure used in geotechnical engineering to determine the potential of soil to expand or shrink due to changes in moisture content. This is particularly important in construction and civil engineering as it helps in understanding how the soil might behave under different weather conditions or when water is introduced, which can affect the stability of structures built on it. The index is usually determined through laboratory tests on soil samples.

How to Calculate Expansion Index?

The following steps outline how to calculate the Expansion Index.

  1. First, determine the final volume (Vf) in cubic meters (m³).
  2. Next, determine the initial volume (Vi) in cubic meters (m³).
  3. Next, gather the formula from above = EI = (Vf – Vi) / Vi.
  4. Finally, calculate the Expansion Index.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

final volume (Vf) = 50 m³

initial volume (Vi) = 30 m³