Enter the percentage of votes for the party and the percentage of seats won by the party into the calculator to determine the Gallagher Index. This calculator can also evaluate any of the variables given the others are known.

## Gallagher Index Formula

The following formula is used to calculate the Gallagher Index.

GI = sqrt((0.5) * (Vp^2 - Vs^2))

Variables:

- GI is the Gallagher Index
- Vp is the percentage of votes for the party
- Vs is the percentage of seats won by the party

To calculate the Gallagher Index, square the percentage of votes for the party and the percentage of seats won by the party. Subtract the square of the percentage of seats from the square of the percentage of votes. Multiply the result by 0.5, then take the square root of the result.

## What is a Gallagher Index?

The Gallagher Index, also known as the least squares index, is a measure used in political science to quantify the discrepancy between the percentage of votes a party receives and the percentage of seats it is awarded in a legislative body. It is used to assess the proportionality of an electoral system. The lower the Gallagher Index, the more proportional the system is considered to be.

## How to Calculate Gallagher Index?

The following steps outline how to calculate the Gallagher Index:

- First, determine the percentage of votes for the party (Vp).
- Next, determine the percentage of seats won by the party (Vs).
- Next, gather the formula from above = GI = sqrt((0.5) * (Vp^2 – Vs^2)).
- Finally, calculate the Gallagher Index.
- 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.

percentage of votes for the party (Vp) = 40%

percentage of seats won by the party (Vs) = 30%