The math
How the Elo rating system works
The Elo system, named after physicist Arpad Elo, turns a rating gap into an expected result. Before a game it predicts your expected score, a number between 0 and 1, from the difference between the two ratings:
E = 1 / (1 + 10 ^ ((Ro - Rp) / 400))
Here Rp is your rating and Rois your opponent's. Equal ratings give an expected score of exactly 0.5, and every extra 400 points of edge pushes the expected score up toward roughly 0.909, about a 91% share. After the game your rating moves by:
change = K * (S - E)
S is the actual result, scored as 1 for a win, 0.5 for a draw and 0 for a loss. If you outscore your expectation you gain points; if you fall short you lose them. The size of the swing is set by K, the K-factor.
K-factor
FIDE K-factor rules
The K-factor controls how quickly a rating reacts to results. New and improving players use a high K so their rating finds its level fast, while established and elite players use a low K so a single game barely moves them. FIDE sets it by three rules:
- K = 40 for a player new to the rating list until they have completed 30 rated games, and for all juniors under 18 as long as their rating stays below 2300.
- K = 20 once a player has an established rating below 2400. This is the standard factor for the large majority of rated players.
- K = 10 once a player has reached a published rating of 2400 or more at any point, even if it later drops below 2400. The strongest players keep this low factor for stability.
Performance
What a performance rating is
A performance rating summarizes how you played across a whole tournament or set of games, rather than one at a time. The FIDE method is simple: take the average rating of your opponents, then add a bonus or penalty dp that comes from your score percentage.
performance = average opponent rating + dp(score %)
The dp value comes from the official FIDE table. Scoring exactly 50% adds nothing, so your performance equals the average opponent. A perfect 100% caps the bonus at +800, and a 0% score bottoms out at -800. For example, scoring 75% against opponents who average 2000 gives a performance rating of 2000 + 193 = 2193. Enter your games in the performance rating tab above to get the number for your own results.
Online vs FIDE
Why online ratings differ from FIDE
Online platforms and FIDE maintain separate rating pools. Lichess uses Glicko-2, which accounts for uncertainty in a rating; it does not simply choose a fixed Elo K-factor. See Lichess’s rating explanation.
There is no universal conversion between these systems. Compare your progress within the same platform and time control. A rating difference across sites does not by itself measure an improvement or a decline in your play.
FAQ
Frequently asked questions
How is chess Elo calculated?
Elo compares two ratings to predict a result, then adjusts them based on what actually happened. Your expected score is E = 1 / (1 + 10^((Ro - Rp) / 400)), where Rp is your rating and Ro is the opponent's. After the game your rating moves by K * (S - E), where S is the result (1 for a win, 0.5 for a draw, 0 for a loss) and K is your K-factor. If you score better than expected you gain points, and if you score worse you lose them.
What is the K-factor in chess?
The K-factor sets how much a single game can move your rating. A higher K means faster changes. FIDE uses K = 40 for new players in their first 30 rated games and for juniors under 18 rated below 2300, K = 20 for established players rated below 2400, and K = 10 once a player has reached a published rating of 2400 or higher. The lower factor for strong players keeps their ratings stable.
How many rating points do you gain for a win?
It depends on the gap and your K-factor. Beating an equally rated opponent with K = 20 gains 10 points, because your expected score was 0.5. Beating a much stronger opponent gains close to the full K, while beating a much weaker one gains only a point or two, since a win was already expected. Use the rating change tab above to see the exact number for any matchup.
How do you calculate performance rating in chess?
FIDE performance rating is the average rating of your opponents plus a bonus or penalty based on your score percentage. You look up the percentage in the FIDE table to get a rating difference dp, then add it to the average opponent rating. A 50% score adds nothing, a perfect score adds 800 and a zero score subtracts 800. The performance rating tab above does this for you across any list of games.
Why is my Chess.com or Lichess rating different from my FIDE rating?
They are separate rating pools with different systems and time controls. Lichess uses Glicko-2, which accounts for rating uncertainty; it is not a fixed-K Elo update. There is no universal conversion to a FIDE rating. Compare results within the same pool and time control.
Can your Elo rating go down?
Yes. If you score worse than your expected score, S is less than E and the rating change K * (S - E) is negative. Losing to a lower-rated player costs the most points, because you were expected to win. Drawing a much stronger opponent can still gain points, since a draw beats the low expected score.
What is a good chess Elo rating?
It is relative to the pool. In FIDE terms a rating around 1200 to 1400 is a solid club beginner, 1600 to 1800 is a strong club player, 2000 is an Expert, 2200 to 2300 is around Candidate Master and FIDE Master, and 2500+ is Grandmaster territory. Online ratings sit on their own scales, so compare within the same site rather than across them.
Keep going
Numbers tell you where you stand; a game review tells you why. Run a free chess game review to see the accuracy, blunders and turning points behind your rating, or read up on chess notation to follow along with any game.
See what is moving your rating
The calculator shows the points. A free chess game review shows the reasons: your accuracy, the blunders that cost you and the best moves you missed, straight from Stockfish.
Review your games free