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Elo rating calculator

The classic Elo formula: your rating, a K-factor and your games give each game's expected score, your rating change, your new rating and your performance in the event.

Your rating

K-factor

K sets how far one game moves a rating. FIDE uses 40, 20 or 10 depending on the player; US Chess once used 32, 24 or 16.

Games

Your opponent's rating and your result, one game per row.

  1. Game 1: result

Press Enter in a rating to move to the next game; at the last one it adds a new game.

Result

Your result appears here as you type.

  • Your rating before the games.
  • At least one game: the opponent's rating and your result.

How it is calculated

This is Arpad Elo's rating method in its logistic form, the shape most rating systems are built on.

  1. Expected score. Against each opponent, your expected score is

    E = 1 / (1 + 10(opponent − you) / 400)

    Equal ratings expect 0.5. Against someone 400 points stronger you expect 1 in 11, about 0.09.
  2. Rating change. Your rating moves by K × (score − expected), added up over the games, with 1 for a win, ½ for a draw and 0 for a loss. Beating a player you were expected to beat earns little; beating a much stronger one earns nearly K.
  3. K-factor. K sets how far one game can move a rating. A high K suits a new player whose rating is still settling; a low K keeps an established rating steady.
  4. Performance rating. The rating at which your results were exactly as expected: a player of that rating would neither gain nor lose points from these games. It is found by trying ratings until the expected scores add up to your score. A perfect or a zero score has none.

Rating bodies change the details. FIDE reads expected scores from a table and rounds the change; US Chess sets K from your number of games and adds a bonus. For those ratings, use the FIDE rating calculator or the US Chess rating calculator.

Frequently asked questions

What K-factor should I use?
The one your rating system uses. FIDE uses 40 for new players and for juniors rated under 2300, 20 below 2400, and 10 once a player has reached 2400. For a FIDE or US Chess rating, use those calculators: each body changes the classic formula in its own way.
Why can my federation's number be different?
Federations adjust the classic method. FIDE reads expected scores from its own table, counts big rating gaps as 400 points for most players and rounds the change to a whole number. US Chess sets K from your rating and number of games and adds a bonus for an unusually strong event.
What is a performance rating?
The rating at which your results in an event were exactly what the formula expected, so a player of that rating would neither gain nor lose points from them. With every game won, or every game lost, no rating fits, so none is given.

Official source