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:

  1. First, determine the player's current Elo Rating (ER).
  2. Next, determine the opponent's Elo Rating (OR).
  3. Next, calculate the expected score (ES) using the formula ES = 1 / (1 + 10^((OR - ER) / 400)).
  4. 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).
  5. 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