Elo Rating Calculator

How Elo works

The Elo system, adopted by FIDE in 1970, predicts the score of each game from the rating difference and then adjusts both ratings according to how the result compares with the prediction. The expected score for a player is 1 ÷ (1 + 10^(D ÷ 400)), where D is the opponent's rating minus the player's. Equal ratings give an expectation of 0.5; a player 100 points stronger is expected to score 0.64, 200 points stronger 0.76 and 400 points stronger 0.91. The rating change is K × (actual score − expected score), summed over all games in the rating period.

A worked example

A player rated 1985 plays seven games in a weekend open against opponents rated 1912, 2048, 1987, 2105, 1950, 2061 and 2010, and scores 4½: three wins, three draws and a loss to the 2105. The expected scores add up to 3.25, so the player outscored expectation by 1.25 points. With K = 20, the rating rises by 20 × 1.25 = 25.0 points, to about 2010. The draw against the 2048 was worth +1.8 and the loss to the 2105 cost −6.7, much less than a loss to an equal opponent would, because the higher-rated player was expected to win. A common misconception is that beating a weaker player gains nothing; it gains a little, but a loss to that player costs a lot.

Choosing K

The K-factor sets how fast ratings move. Under FIDE's regulations it is 40 for new players until they have 30 rated games, and for juniors until the end of the year of their 18th birthday while their rating is under 2300. It is 20 for everyone else rated under 2400, and 10 once a player's published rating has reached 2400, permanently, even if it later falls. The same tournament at K = 40 would gain about 50 points. There is also a cap: if K × the number of games in a rating period exceeds 700, K is reduced so that the product does not exceed 700, which stops very active juniors' ratings jumping by hundreds of points in a month.

The 400-point rule

To stop strong players losing rating for beating much weaker ones, FIDE treats any rating difference over 400 points as exactly 400 for players rated below 2650. That caps the stronger player's expected score at 0.91, so a win still gains 0.9 points times K. Since October 2025, players rated 2650 and above use the full difference. FIDE's official expected scores come from a lookup table based on the normal distribution rather than the logistic formula used here; the two differ by at most about 0.01 per game, a fraction of a rating point at K = 20.

How to use it

1. Enter your current rating.
2. Let the calculator choose K from your age, number of rated games and peak rating, or set it yourself.
3. Enter each opponent's rating and your result, round by round.
4. Read the expected score, the change for each game and your new rating.