How FIDE ratings are calculated
The FIDE rating system is a practical Elo-style system designed to estimate a player’s strength from game results, not to define a player’s absolute ability. The key idea is simple: if you score better than the system expected against your opponents, your rating goes up; if you score worse, it goes down. FIDE’s published regulations turn that idea into a very specific process built around the expected score, the score difference after each game, and a development coefficient called the K-factor.
For a single game, the rating update is written in display form as
Here ΔR is the rating change, K is the development coefficient, S is the actual score for the game, and E is the expected score.
FIDE publishes the expected-score calculation through a table of rating differences.
In the usual Elo interpretation, the same idea is often expressed with a smooth logistic curve.
That formula says that when two players have equal ratings, each is expected to score 1/2.
If the opponent is rated higher, your expected score falls below 1/2; if the opponent is rated lower, your expected score rises above 1/2.
The 400-point scale is a convention that makes rating gaps translate into readable changes in expected score.
A 200-point rating gap is meaningful but not decisive, while a 400-point gap implies a strong statistical favorite.
FIDE's practical regulations then apply the development coefficient.
As of the current regulations, the published values used by FIDE are typically K = 40 for a new player until they have completed events with at least 30 games, K = 20 while the published rating remains below 2400, and K = 10 once a player has reached 2400 and remains there.
That means the same result can move two players by different amounts even if they played the same opponent and scored the same result.
This design matters: a new player is allowed to move faster because the system has less historical evidence, while a long-established elite player moves more slowly because the rating should not whipsaw around after a single upset.
The single-game update can also be expanded into a multi-game event.
If a player contests several rated games in one tournament, each game contributes to the total score and the total expected score.
The final event change is still driven by the same basic logic: if you overperform relative to expectation, your rating increases; if you underperform, it decreases.
The regulations also include special handling for unrated players and initial rating assignment, which is separate from ordinary rating change.
For example, the initial rating procedure uses the average rating of rated opponents.
It applies the rules in the regulations for players entering the list for the first time.
Here is a fuller classical-tournament example using the exact conditions you asked for.
Suppose a player enters a FIDE-rated classical tournament with an initial published rating of R_player = 1892, and the tournament uses K = 40.
First, compute the expected score.
Second, record the actual score. Because the player won, the result is S = 1.
Third, add the change to the starting rating.
After rounding to the nearest whole number, the player's new published rating would be approximately 1919.
The same example shows why the K-factor matters: if the player had instead been on K = 20, the gain would have been roughly half as large, about 13.6 points.
Now consider an established 2400-rated player under the K = 10 regime.
If that player beats a 2400-rated opponent, the expected score is 0.5, so the gain is only 5 points.
That modest swing is intentional.
One useful way to think about FIDE ratings is to separate the mathematics from the tournament policy.
There are a few consequences of this structure.
It is also important not to confuse FIDE rating with performance rating.
Reference basis: FIDE Rating Regulations.