How to use it
- Type the Rating of player A and the Rating of player B before the game.
- Choose the Result for player A, and check the K factor: 20 is the FIDE value for most players under 2400.
- Read the New rating and the Change for each player.
- For a tournament, list each game in Tournament games as opponent rating | score. The change is worked out from the ratings before the event.
How the expected score and the change are calculated
The expected score is the share of the points a player should win against an opponent, from the difference between the two ratings. A player 100 points stronger is expected to score 64 %, and one 200 points stronger 76 % (Wikipedia, Elo rating system). The rating change is the K factor multiplied by the sum of the differences between the actual and the expected score.
FIDE rounds the rating change of a rating period to a whole number, with 0.5 rounded away from zero (FIDE handbook, B.02 Rating Regulations, section 8.3.4). This calculator rounds each change the same way.
Expected score: E = 1 ÷ (1 + 10^((Rb − Ra) ÷ 400))
Change: K × (score − E), summed over the games
Example: A rated 1600 beats B rated 1400, K 20
E(A) = 0.760, change = 20 × (1 − 0.760) = 4.8, rounded to 5- FIDE's K factor depends on the player: 40 for a new player until 30 games are completed, and for a player under 18 whose rating is below 2300 until the end of the year of the 18th birthday; 20 for a rating below 2400; 10 once a rating of 2400 has been reached (FIDE handbook, B.02, section 8.3.3). The default here is 20.
- FIDE takes the expected score from a table of rating differences rather than the formula, so its changes can differ by a point. From 1 October 2025 FIDE also counts a difference over 400 points as 400 for players below 2650; this page does not apply that rule.
What this calculator does not include
- The initial rating of a new player, which FIDE works out in section 8.2 of its handbook.
- Performance ratings and the ratings of unrated players.
- Other federations and online systems, which use their own K factors and rules.
Worked example: 1600 against 1400, a win, K 20
The expected score of A is 1 ÷ (1 + 10^(−200 ÷ 400)) = 0.76, so the expected score of B is 0.24.
A wins, a score of 1: the change is 20 × (1 − 0.76) = 4.8, rounded to 5, so A goes to 1,605. B scores 0 against an expected 0.24: 20 × (0 − 0.24) = −4.8, rounded to −5, so B goes to 1,395.
| Player A | Player B | |
|---|---|---|
| Rating before | 1,600 | 1,400 |
| Expected score | 0.76 | 0.24 |
| Change | 5 | -5 |
| New rating | 1,605 | 1,395 |
Frequently asked questions
What is an Elo rating?
A number that estimates a player's strength from results alone. After each game the winner takes points from the loser, and the amount depends on the expected score, so an upset moves more points.
Which K factor should I use?
Use the K factor of your federation or event. FIDE uses 20 for most players below 2400, 10 once a player has reached 2400 and 40 for new players; the default here is the common value of 20.
Why is the expected score not exactly the same as FIDE's table?
FIDE looks up its own table of rating differences in its handbook. The table is built on the same idea, so an expected score can differ from the formula used here in the last digit.
How do I calculate a tournament?
List each game with the opponent's rating and your score. The change is the K factor times the sum of the differences, using your rating before the event, and it is rounded to a whole number.
Are these ratings the same as FIDE ratings?
Only if your inputs are FIDE ratings and you apply FIDE's rules. This calculator shows the Elo method; it does not apply the full FIDE rating regulations.
Sources
- Wikipedia: Elo rating system (expected score and the 64 % example)
- FIDE Handbook, B.02 FIDE Rating Regulations (K factor, section 8.3.3; rounding, section 8.3.4)
Figures and text last checked on Tuesday, November 10, 2026.