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))

Variables:

- 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).

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