Enter the length of the semi-major and semi-minor axis into the calculator to determine the eccentricity index. This calculator can also evaluate any of the variables given the others are known.

Eccentricity Index Formula

The following formula is used to calculate the eccentricity index.

EI = sqrt(1 - (b^2 / a^2))


  • EI is the eccentricity index
  • a is the length of the semi-major axis
  • b is the length of the semi-minor axis

To calculate the eccentricity index, square the length of the semi-minor axis and divide it by the square of the length of the semi-major axis. Subtract this result from 1 and then take the square root of the result.

What is an Eccentricity Index?

The Eccentricity Index is a mathematical concept used in graph theory and network analysis. It measures the maximum distance from one vertex to all other vertices in a graph, providing an indication of how ‘eccentric’ or ‘outlying’ a particular point is within the network. In other words, it quantifies the extent to which a node is far away from others in the network. This index can be useful in various fields, including computer science, social network analysis, and transportation planning.

How to Calculate Eccentricity Index?

The following steps outline how to calculate the Eccentricity Index (EI).

  1. First, determine the length of the semi-major axis (a).
  2. Next, determine the length of the semi-minor axis (b).
  3. Next, gather the formula from above = EI = sqrt(1 – (b^2 / a^2)).
  4. Finally, calculate the Eccentricity Index (EI).
  5. After inserting the values of a and b into the formula 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.

Length of the semi-major axis (a) = 5

Length of the semi-minor axis (b) = 3