How the chess rating (FIDE Elo) works
Chess does not have a points table. Every player has a rating, a number that goes up when you score more than expected against your opponents and down when you score less. Beating a much higher-rated player gains a lot; losing to a much lower-rated one costs a lot. The world ranking is the list of players in order of rating.
FIDE publishes a new rating list on the first day of every month. Only ratings of 1400 or more are published.
Very roughly, a rating difference of 200 points means the stronger player is expected to score about 76% against the weaker one.
Expected score
For each game, FIDE looks at the rating difference D between the two players and reads the expected score from its table:
| Rating difference | Higher-rated expected | Lower-rated expected |
|---|---|---|
| 0 to 3 | 0.50 | 0.50 |
| 47 to 53 | 0.57 | 0.43 |
| 99 to 106 | 0.64 | 0.36 |
| 198 to 206 | 0.76 | 0.24 |
| 303 to 315 | 0.86 | 0.14 |
| 392 to 411 | 0.92 | 0.08 |
| more than 735 | 1.00 | 0.00 |
The 400-point rule (from 1 October 2025): for players rated below 2650, any difference over 400 is treated as 400. Players rated 2650 and above use the real difference.
The rating change
For each game: ΔR = score − expected score (score is 1 for a win, 0.5 for a draw, 0 for a loss). Add up ΔR over the tournament or month, then multiply by K:
Rating change = K × ΣΔR, rounded to the nearest whole number (0.5 rounded away from zero).
K, the development coefficient
| Player | K |
|---|---|
| New to the list, until 30 rated games | 40 |
| Until the end of the year they turn 18, while rated under 2300 | 40 |
| Rated under 2400 | 20 |
| Has once reached 2400 (even if they drop below later) | 10 |
If K × number of games in a month would exceed 700, K is cut to the largest whole number that keeps it at 700 or below.
A first rating
A new player gets a published rating after at least 5 games against rated opponents (these can be pooled over up to 26 months). The calculation:
- Ra = the average rating of their rated opponents plus two imaginary 1800-rated opponents, against whom the player is counted as drawing;
- Ru = Ra + dp, where dp comes from FIDE's table converting the player's percentage score into a rating difference (for example 50% → 0, 60% → +72, 70% → +149, 40% → −72);
- the first rating is capped at 2200 and must be at least 1400.
A player who scores zero in their first event has that event ignored.
Which games count
- Each player must have at least 120 minutes for a 60-move game if either player is rated 2400 or more; 90 minutes if either is 1800 or more; otherwise 60.
- Unplayed games and forfeits do not count; a game where both players have made a move does.
- In a match, games played after one player has already won are not rated, and matches against an unrated player are not rated.
- A player with no rated game for a year is listed as inactive; one game makes them active again.
- A player who drops below 1400 is shown as unrated on the next list.
A worked example
Made up to show the arithmetic. An Indian junior rated 1800 (aged 16, so K = 40) plays three games in a month:
| Opponent | Difference | Expected | Result | ΔR |
|---|---|---|---|---|
| 2000 | 200 | 0.24 | Win (1) | +0.76 |
| 1800 | 0 | 0.50 | Draw (0.5) | 0 |
| 1650 | 150 | 0.70 | Loss (0) | −0.70 |
ΣΔR = 0.06. Change = 40 × 0.06 = 2.4, rounded to +2: new rating 1802.
Variations
| Rating | Covered here |
|---|---|
| Standard (classical) | Yes |
| Rapid, blitz | No (separate regulations, same idea) |
| Team rankings (federation averages) | No |