How Elo rating changes are calculated
Every Elo update starts with an expected score — the share of the total score a player is expected to earn, based purely on the rating gap between the two players:
E = 1 / (1 + 10^((Opponent's Rating − Your Rating) / 400)) A 200-point rating advantage corresponds to roughly a 76% expected score; a 400-point advantage, about 91%. With the 400-point cap enabled, rating differences greater than 400 points are treated as 400 points, so the expected score remains about 91%. The new rating is then the old rating adjusted by the gap between what actually happened and what was expected, scaled by the K-factor:
New Rating = Old Rating + K × (Actual Score − Expected Score) Actual score is 1 for a win, 0.5 for a draw, and 0 for a loss. A player who performs better than expected gains rating points, while a player who performs worse than expected loses rating points. The size of the change depends on the difference between the actual and expected scores and the K-factor.
For example, if both players start at a rating of 1500, Player A has an expected score of 50%. With a K-factor of 32, an A win produces a +16 rating change for Player A (new rating 1516) and a −16 change for Player B (new rating 1484).
What K-factor should I use?
The K-factor controls how strongly a game result affects the rating. A higher K-factor means bigger rating changes; a lower one means smaller, more stable changes. There's no single universal value — different rating systems and organizations use different K-factors, often scaled to how established a player is, since new players' ratings are usually allowed to move faster than experienced players'. 32 is a commonly used general-purpose default; lower values like 20 or 10 produce steadier, slower-moving ratings, while higher values like 40 produce bigger swings per game.
The 400-point cap
Some Elo-based rating systems cap the rating difference used in the expected-score calculation at 400 points. Without a cap, very large rating differences produce expected scores increasingly close to 100% or 0%. This calculator offers the 400-point cap as an optional toggle. When enabled, rating differences greater than 400 points are treated as exactly 400 points for the expected-score calculation. Turn it off to use the full rating difference.
Frequently asked questions
How is an Elo rating change calculated?
From the rating gap between two players, an expected score is calculated. It represents the share of the total score each player is expected to earn based on their ratings. After the game, each player's rating shifts by their K-factor multiplied by the difference between what actually happened and what was expected.
Why did I lose points even though I won?
With a positive K-factor, a win always increases your rating under the standard Elo formula because the actual score (1) is greater than the expected score (which is below 1). If the K-factor is 0, there is no rating change. If another rating tool shows a loss after a win, it may be applying additional rules beyond the base Elo formula.
Does this match a specific organization's official rating exactly?
This calculator uses the standard Elo formula for a single game, which is the foundation most rating systems build on. Some organizations layer additional rules on top — different K-factor schedules, rating floors, provisional-rating rules, or tournament-wide calculations — that a single-game calculator won't reproduce exactly. If you need to match a specific organization's rating precisely, check their official rules for any adjustments beyond the base formula.