Elo Rating Calculator

About the Elo Rating Calculator

The Elo rating system is one of the most successful ideas in competitive games. Invented by the physicist and chess master Arpad Elo in the 1950s and adopted by the World Chess Federation in 1970, it gives every player a number that rises when they do better than expected and falls when they do worse. Today it is used far beyond chess, from football and basketball power rankings to esports, table tennis and the matchmaking systems of online games.

This Elo rating calculator works out new ratings after a game. Enter your rating, your opponent's rating, the result and the K-factor, and it gives your new rating, the expected score before the game, your opponent's new rating, the change you would have seen for every possible result, and the size of the rating gap.

How to Use the Elo Rating Calculator

Enter your rating and your opponent's rating before the game.

Choose the result: win, draw or loss.

Choose the K-factor, which sets how much a single game can move a rating. 32 is a common default; FIDE uses 40, 20 or 10 depending on experience and rating.

How Elo Ratings Are Worked Out

  expected score  E  =  1 ÷ (1 + 10^((opponent − you) ÷ 400))
  actual score    S  =  1 for a win, 0.5 for a draw, 0 for a loss
  change             =  K × (S − E)
  new rating         =  old rating + change

Step-by-Step Example

A 1500 player beats a 1700 player, K = 32.

  Expected:   1 ÷ (1 + 10^((1700 − 1500) ÷ 400))   =  1 ÷ (1 + 3.162)  =  0.240
  Change:     32 × (1 − 0.240)                     =  +24.3
  New:        1500 + 24.3                          =  1524
  Opponent:   1700 − 24.3                          =  1676

With the same ratings, a draw would move the lower-rated player up by 8.3 points and a loss down by 7.7.

Expected Score and Rating Gaps

The expected score is the share of points a player is predicted to take from a game or match, counting draws as half. It is not quite the chance of winning, because in games like chess many games end in draws. A 400-point gap means the stronger player is expected to score about 91 percent, winning or drawing almost every game.

Why Upsets Move Ratings Most

The system rewards results relative to expectation. Beating a much stronger player was unlikely, so it earns many points; beating a much weaker one was expected, so it earns few. Likewise, losing to a weaker player costs a lot, and losing to a stronger one costs little. Over many games, a player's rating settles at the level where their results match expectations — which is what makes Elo a good measure of current strength.

The K-Factor

The K-factor is the largest possible change from one game. A high K makes ratings responsive, useful for new players whose true strength is unknown; a low K makes them stable, suitable for established players. FIDE uses K = 40 for players new to the rating list and for juniors under 2300, K = 20 for players below 2400, and K = 10 once a player has reached 2400. Online platforms often use their own systems derived from Elo, such as Glicko, which also track how uncertain a rating is.

Ratings and Titles in Chess

A beginner might be rated around 800 to 1200, a strong club player around 1800 to 2000, and an expert above 2000. International Master and Grandmaster titles require ratings of about 2400 and 2500 respectively, along with qualifying tournament results. The very best players in the world are rated above 2700, and the highest classical rating ever achieved is just over 2880.

Elo Beyond Chess

Sports analysts use Elo-style ratings to rank football, basketball and American football teams, often adding adjustments for home advantage and the margin of victory. Video games use it for matchmaking, pairing players of similar skill so games are competitive. Wherever results can be compared head to head, Elo offers a simple, self-correcting ranking.

Provisional Ratings

New players do not start with an established rating. Many systems give a provisional rating based on the first few games — often calculated from the average rating of the opponents plus an adjustment for the score — and use a higher K-factor until the player has completed a set number of games. This lets a new player's rating move quickly to the right level instead of taking dozens of games to get there. Some online platforms show a question mark next to a provisional rating until enough games have been played.

Rating Inflation and Deflation

Because points move between players, the average rating of a pool stays roughly the same over time. But when many improving young players join, win points and then leave, or when rating floors stop ratings falling below a set level, the average can drift. That is why ratings from different organisations, countries or online sites cannot be compared directly, and why historical ratings from different decades are not perfectly comparable either.

Understanding Your Result

New rating gives your rating after the game and the change.

Expected score shows your predicted score against this opponent.

Opponent gives your opponent's new rating.

Every result shows the change for a win, a draw and a loss.

Rating gap shows the difference between the ratings.

Worth knowing explains why upsets move ratings most.

When Should You Use This Calculator?

After a rated chess game or tournament round.

Running a club ladder or league rating system.

Estimating how a result will change your rating.

Building Elo rankings for a sports league.

Understanding matchmaking in online games.

Common Mistakes

Using ratings from after the game instead of before.

Mixing K-factors between players without adjusting.

Reading the expected score as a win probability.

Comparing ratings from different rating systems.

Judging strength from very few games.