Enter the old Elo rating, K-factor, actual score, and expected score into the calculator to determine the new Elo rating.

## Elo Rating Formula

The following formula is used to calculate the Elo rating change after a game:

R_new = R_old + K * (S - E)

Variables:

- R_new is the new Elo rating
- R_old is the old Elo rating
- K is the K-factor, which determines the impact of the game on the rating
- S is the actual score of the player (1 for a win, 0.5 for a draw, 0 for a loss)
- E is the expected score of the player based on the ratings of the players involved

To calculate the new Elo rating, add the product of the K-factor and the difference between the actual score and the expected score to the old Elo rating.

## What is an Elo Rating?

The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. Named after its creator, Arpad Elo, a Hungarian-American physics professor, the Elo system is based on the concept that the performance of each player in a game is a normally distributed random variable. The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to win an equal number of times.

## How to Calculate Elo Rating?

The following steps outline how to calculate the Elo Rating:

- First, determine the player’s current Elo Rating (ER).
- Next, determine the opponent’s Elo Rating (OR).
- Next, calculate the expected score (ES) using the formula ES = 1 / (1 + 10^((OR – ER) / 400)).
- Next, determine the actual score (AS) based on the outcome of the game (1 for a win, 0.5 for a draw, 0 for a loss).
- Finally, calculate the new Elo Rating using the formula: NER = ER + K * (AS – ES), where K is the K-factor that determines the impact of the game result on the rating change.

**Example Problem:**

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

Player’s current Elo Rating (ER) = 1500

Opponent’s Elo Rating (OR) = 1600

Expected score (ES) = 0.359935

Actual score (AS) = 1 (win)

K-factor (K) = 32