# How will my chess rating change?

Computes a chess rating change with the Elo formula and the FIDE K factors from your rating and each game’s opponent rating and result.

- Page: https://www.acalculator.org/game/chess-rating-calculator
- JSON spec: https://www.acalculator.org/game/chess-rating-calculator.json
- Version: d49c1580d61d

## Default answer

Example with the default inputs (Your rating 1,500, K factor 20, Games [Opponent rating 1,700, Result Win]): With a rating of 1,500 and K = 20, your rating changes by 15 to 1,515.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| r | Your rating | Your rating before the games. |
| k | K factor | FIDE: 40 for a new player (under 30 games), or rated below 2300 until the end of the year of the 18th birthday; 20 below 2400; 10 once 2400 has been reached. |
| kc | Your K factor | The K factor your federation or site uses, for example 32. |
| games | Games | One row per game: the opponent’s rating and your result. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| change | Rating change | K × (score − expected score), rounded to the nearest whole number (halves away from zero). |
| newRating | New rating | Your rating plus the rounded change. |
| exactChange | Change before rounding | K × (score − expected score), before rounding. |
| score | Your score | Wins count 1, draws 0.5, losses 0. |
| expected | Expected score | The sum over the games of 1 ÷ (1 + 10^(−D ÷ 400)), where D is your rating minus the opponent’s. |
| kUsed | K factor used | The K factor, lowered when K × games would pass 700 (FIDE rule). |
| count | Games | How many games are counted. |

## Method

Expected score per game = 1 ÷ (1 + 10^(−D ÷ 400)), D = your rating − opponent rating (at most ±400 below 2650); change = K × (total score − total expected score), rounded; K ≤ 700 ÷ games.

## Assumptions

- The expected score comes from the Elo formula. FIDE reads it from its own table (rating regulations 8.1.2), rounded to two decimals, so an official FIDE change can differ from this one by a fraction of a point per game.
- All games are in one rating period, scored against your rating before the games.

## Worked examples

1. r = 1,500, k = 20, games = {"opponent":1700,"result":"1"} or undefined gives expected = 0.240253, exactChange = 15.194939, change = 15, newRating = 1,515. Source: Glickman and Doan, The US Chess Rating System, US Chess, 2026, section 4.2 (winning expectancy). https://new.uschess.org/sites/default/files/media/documents/us_chess_rating_system_specs-2026-04-06.pdf; FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024.
2. r = 2,100, k = 20, games = {"opponent":2100,"result":"0.5"} or {"opponent":2300,"result":"0"} gives expected = 0.740253, exactChange = -4.805061, change = -5, newRating = 2,095. Source: FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024.
3. r = 1,500, k = 20, games = {"opponent":2100,"result":"0"} or undefined gives expected = 0.090909, change = -2. Source: FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024 (8.3.1, the 400-point rule).
4. r = 2,700, k = 10, games = {"opponent":2200,"result":"1"} or undefined gives expected = 0.94676, change = 1. Source: FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024 (8.3.1).
5. r = 1,500, k = 40, games = {"opponent":1500,"result":"1"} or {"opponent":1500,"result":"1"} gives kUsed = 25, expected = 13.5, exactChange = 12.5, change = 13. Source: FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024 (8.3.3 K × n ≤ 700, 8.3.4 rounding).
6. r = 1,500, k = 40, games = {"opponent":1500,"result":"1"} or {"opponent":1500,"result":"1"} gives exactChange = -12.5, change = -13, newRating = 1,487. Source: FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024 (8.3.4).

## FAQ

### How is a chess rating change calculated?

For each game, the Elo formula gives your expected score, 1 ÷ (1 + 10^(−D ÷ 400)), where D is your rating minus your opponent’s. Your rating changes by K × (your score − your expected score), added up over the games. A 1500 player expected to score 0.24 against a 1700 player gains 20 × (1 − 0.24) = 15 points for a win.

### What K factor should I use?

FIDE uses 40 for a player new to the rating list until 30 games are completed, and for players rated below 2300 until the end of the year of their 18th birthday; 20 for other players rated below 2400; and 10 once a player’s published rating has reached 2400, even if it drops later. Pick Other for a federation or site that uses a different K, such as 32.

### What is the 400-point rule?

Under FIDE’s rules, for a player rated below 2650, a rating gap of more than 400 points counts as exactly 400. So beating a much weaker player never earns less than the 400-point amount, and losing to a much stronger one never costs more.

### Why does winning against a stronger player give more points?

Your expected score against a stronger player is low, so a win beats the expectation by a lot. Against a much weaker player you are expected to win, so a win adds little and a loss costs a lot.

### Why can my result differ slightly from the official FIDE change?

FIDE reads the expected score from a table of rating differences rounded to two decimals, based on the normal distribution, while this calculator uses the Elo formula. The two agree closely, so the difference is a fraction of a point per game.

### Does this work for chess.com or lichess ratings?

Those sites use the Glicko or Glicko-2 systems, which also track how certain a rating is, so their changes differ. This calculator follows the Elo method used by FIDE and many national federations.

## Sources

- FIDE Handbook B.02, FIDE Rating Regulations effective 1 March 2024, section 8.3 (the 400-point rule for players below 2650 effective 1 October 2025). https://handbook.fide.com/chapter/B022024
- Glickman and Doan, The US Chess Rating System, US Chess, 2026, section 4.2 (standard winning expectancy). https://new.uschess.org/sites/default/files/media/documents/us_chess_rating_system_specs-2026-04-06.pdf