The Elo rating system is used for two player games as well as multiplayer competitions. It was created by Arpad Elo, an American physics professor. Before Elo system was introduced, a numerical rating device was used for players to track their individual performance. It was known as the Harkness system. The Harkness system was not accurate always and so Elo made this new system with a strong statistical basis. The system became popular fast and soon USCF and FIDE switched to the Elo rating system. The Elo rating system generally refers to a chess player’s rating calculated by FIDE.

Elo results are calculated at the end of every tournament. This is done for every participant and a Final Standings Table is created. The table contains the chess players' names, their current ratings at the beginning of the day and tournament and Elo results after the tournament.

The Final Standings Tables are then passed on to FIDE and FIDE calculates the final Elo result for every individual player. It makes the corrections in case of any mistake and creates a database for all the players, which are then published on the Internet and are updated quarterly.

For most of the chess players around the world, FIDE ratings are the most important. The list of this rating is published four times every year. Following are the rating analysis of FIDE till 2006:

Rating between 2200 and 2399: There are 17171 players who have the rating between 2200 and 2399. These players are usually affiliated with the Candidate Master title.

Rating between 2400 and 2499: There are around 1868 players who have a rating of 2400 to 2499. These players are generally the winners of IM or GM title.

Rating between 2500 and 2599: Around 563 players have a rating of 2500 to 2599. Most of these players have the GM title.

Rating between 2600 and 2699: There are around 123 players who have a rating of 2600 to 2699. Almost all of them have the GM title.

Rating between 2700 and 2799: There are only18 players who have a rating of 2700 to 2799.

Rating of 2800 and more: There are only four players who have a rating of 2800 or more. They are namely Garry Kasparov, Vladimir Kramnik, Veselin Topalov and Viswanathan Anand. Garry Kasparov has the highest ever FIDE rating of 2851.

To check FIDE rating Calculators:

• Calculator for FIDE rated players who want to check rating change after the game with FIDE rated opponent.
  Rating Change calculator.
• Calculator for chess players who has not got FIDE rating. Players can check their rating performance.
  Rating Performance calculator.
• Calculator for unrated players who can get information of their future FIDE rating based on one or several rating performances.
  Initial Rating calculator

Performance rating is often calculated as: Performance Rating = Opponents' Average + Performance Change. The performance rating often depends upon the average of a player’s opponent and the performance of that player. It is very important to have performance rating to get the Grandmaster and International Master Norms.

The chess ratings are based on the results of the championship and not on the performance of the players. According to the Elo rating scales, a difference of 200 points means that the stronger player has a score of 0.75 approximately. The player’s expected score is determined by adding the probability of his winning and half the probability of his drawing. Thus, the expected score of 0.75 is represented as 75% chance of winning and 25% chance of losing and 0% chance of tying.

If Player A has true strength RA and Player B has true strength RB, the exact formula (using the logistic curve) for the expected score of Player A is:

Similarly the expected score for Player B is:

and

where         and   

Note that the same denominator applies to both expressions. This means that by studying only the numerators, we find out that player A has about QA / QB times greater chance of winning as player B. It then follows that for each 400 rating points of advantage over the opponent, the chance of winning is magnified ten times in comparison to the opponent's chance of winning.

Also note that EA + EB = 1. In practice, since the true strength of each player is unknown, the expected scores are calculated using the player's current ratings.

The Final Standings Tables are then passed on to FIDE and FIDE calculates the final Elo result for every individual player. It makes the corrections in case of any mistake and creates a database for all the players, which are then published on the Internet and are updated quarterly.

There are also other rating systems besides Elo, which are used in different parts of the world. Some of them are not even in use at the present time, as they have been discarded for the Elo rating system. Some of these rating systems are:

• The Ingo system: Anton Hoesslinger designed this. It was used by West German Chess Federation from 1948-1992.
• The Harkness System: It was invented by Kenneth Harkness in the year 1956. it was used by USCF from 1950 to 1960.
• British Chess Federation Rating System: It was introduced in the year 1958.
• Correspondence Chess League of America Rating System: This is no more in use as the Correspondence Chess League of America now uses Elo.
• TrueSkill ranking system: This is the latest rating system introduced in the year 2005 by Xbox Live online gaming service. This system is an extension of Glickman's system for rating the players in to multi-player and multi-team games.
• Glicko rating system: It was invented by Mark E. Glickman, as a substitute of the Elo rating system.
• Chessmetrics: It was invented by Jeff Sonas. It is considered to be more accurate than the Elo system and is based on computer analysis of a large database of games.

Live rating calculates a player’s rating after every game unlike FIDE, which updates its rating list every three months. Live rating is calculated based on the FIDE ratings published previously. Though Live rating is not yet official, it has caught the attention of many players in the year 2008. These Live ratings are maintained by Hans Arild Runde and published at http://chess.liverating.org

Over the last few years, chess software has emerged to be stronger than the human players. The performances of the chess software cannot be rated accurately. However, these engines are rated on the performance of the program they are based on.

The chess engines are rated by using Elo system, which has no direct association with FIDE or other federations which rate human players. It’s necessary for a top chess machine to have the highest ratings, as the top human chess players.