Elo rating calculator
Enter your rating and your opponent, get the expected score and the new rating.
How does the Elo formula work?
Your expected score against an opponent is E = 1 ÷ (1 + 10^((opponent rating − your rating) ÷ 400)); a win scores 1, a draw 0.5 and a loss 0. Your new rating is the old one plus K × (score − expected score). Rated 1500 against a 1600 opponent, you are expected to score 0.36, so with K = 20 a win gains 20 × (1 − 0.36) = 12.8 points and a loss costs 7.2.
Does FIDE use that formula?
Not exactly. The FIDE Rating Regulations (Handbook B.02, section 8.1.2) give expected scores in a table: a rating difference of 100 points is 0.64 for the higher-rated player, 200 points is 0.76 and 400 points is 0.92. The logistic formula gives 0.640, 0.760 and 0.909. The FIDE table matches a normal distribution curve (we checked it to within 0.01), so the two agree closely for small differences and drift apart for large ones. This page uses the FIDE table by default and can switch to the logistic formula.
What K-factor does FIDE use?
K is 40 for a player new to the rating list until they have completed events with at least 30 games, and for all players until the end of the year of their 18th birthday while their rating stays under 2300; 20 while the rating is under 2400; and 10 once the published rating has reached 2400, even if it later drops below. If K times the number of games in a rating period exceeds 700, K is lowered to the largest whole number that keeps it at 700 or less: 38 instead of 40 for 18 games.
What is a performance rating?
The average rating of your opponents plus a rating difference read from FIDE’s table 8.1.1 for your percentage score. A score of 4.5 out of 7 is 64%, which the table turns into +102, so against opponents averaging 1800 the performance is 1902. A perfect score or a zero is shown in the table as a notional +800 or −800.
Worked example: a five-round tournament
A player rated 1800 with K = 20 plays opponents rated 1750, 1850, 1900, 1700 and 2000, winning two games, drawing two (against 1850 and 2000) and losing to the 1900. The score is 3 out of 5. The expected scores from the FIDE table add up to 2.24, so the change is 20 × (3 − 2.24) = +15.2 points, which is rounded to +15 for the new rating of 1815. The average opponent is 1840, the score is 60%, and the table gives a rating difference of +72, so the performance rating is 1912. With the logistic formula the change would be +15.2, almost the same, because the rating differences here are small.
Why does a win over a weaker player earn so little?
Because the system rewards surprise. A player rated 2000 against a 1600 opponent has an expected score of 0.92 (a 400-point gap), so with K = 20 a win gains only 1.6 points, while a loss costs 18.4. For the 1600 player the numbers are mirrored: a win is worth 18.4 points and a loss costs 1.6. Over many games this keeps ratings in line with results, and beating much weaker opponents does little for a rating.
Common mistakes with rating calculations
Using the wrong K for the player: the same results move a rating by twice as much at K = 40 as at K = 20. Entering the opponent rating of the wrong game, or entering draws as 1 instead of 0.5. Applying one game at a time and then re-rating after each, when FIDE computes a whole rating period at once from the rating at the start of it. Expecting a performance rating to equal a new rating: it describes the event only. Comparing this FIDE-style result with the number shown by an online platform, which uses its own system.
Do USCF, chess.com or Lichess use the same rules?
No. This page follows the FIDE scheme. Other federations and online platforms use their own K rules, rating floors and formulas, so a rating from another system will not change by the same amount. One FIDE rule to note: since 1 October 2025 a rating difference of more than 400 counts as 400 for players rated below 2650, while players rated 2650 and above use the full difference.
An expected score is a probability-like number between 0 and 1. To turn betting odds into the probability they imply, use the odds calculator.
Sources: FIDE Handbook, B.02 FIDE Rating Regulations (effective from 1 March 2024), sections 8.1.1, 8.1.2, 8.2.3, 8.3.1 (amendment effective 1 October 2025), 8.3.3 and 8.3.4. Check the Handbook for later changes. How we check our calculators.