An Elo rating changes when your actual result differs from the score expected against your opponent. Beating a stronger-rated opponent normally gains more than beating a weaker-rated one under the same K-factor. A draw can gain or lose points because its value depends on the expectation before the game.
The two parts of the formula
For a generic Elo estimate, first calculate expected score:
E = 1 / (1 + 10^((opponent rating − your rating) / 400))
Then calculate the change:
Change = K × (actual score − E)
New rating = old rating + change
Actual score is 1 for a win, 0.5 for a draw, and 0 for a loss. K controls the size of an update. A bigger K produces a larger change from the same result.
Example: equally rated players
Suppose both players are rated 1500 and your K-factor is 20. The rating difference is zero, so expected score is 0.5.
| Result | Calculation | Change | New rating | | --- | --- | --- | --- | | Win | 20 × (1 − 0.5) | +10 | 1510 | | Draw | 20 × (0.5 − 0.5) | 0 | 1500 | | Loss | 20 × (0 − 0.5) | −10 | 1490 |
These are hypothetical examples using generic Elo, not recorded player outcomes.
Example: a stronger opponent
Keep your rating at 1500 and K at 20, but make the opponent 1700. Expected score is approximately 0.2403.
A win gains about 15.19 points; a draw gains about 5.19; a loss costs about 4.81. The draw gains points because half a point exceeds the expected score. Use the Elo calculator to change the inputs and compare outcomes.
Expected score is not win probability
A 24% expected score means an average of roughly 0.24 points per game against that rating difference in the model. It does not mean exactly a 24% chance of winning. Draws also contribute points. Elo expectation alone does not uniquely split the chances into win, draw and loss.
Why your platform may show a different change
The calculator on this site implements the simple formula above. It does not include the full official FIDE rules or the additional uncertainty measures used by Glicko systems. Lichess explains that Chess.com and Lichess use different rating systems and that ratings from separate playing pools are not directly interchangeable. See its rating-system overview.
Even in an Elo setting, different players can have different K-factors, so their point changes do not necessarily cancel exactly. For an official FIDE calculation, consult the applicable FIDE rating regulations and their effective date rather than assuming the generic estimate is exact.
Use the number for the right decision
A rating summarizes results within a particular pool and system. It does not explain why a game was lost or identify a tactical weakness. For that, review the game itself.
Calculate a generic Elo change, then use game review to turn a result into a concrete study question.