Elo Rating Calculator
Enter two ratings, the result for player A and a K-factor. This tool returns the Elo expected score and the rating points the result produces — an internal weighting of the rating system, not a forecast of who will win.
Model: logistic Elo, 400-point scale • Checked 24 Aug 2026Enter the game
| Quantity | Player A | Player B |
|---|
The expected score is how the rating system weights the result, not a prediction of who will win.
How the rating update is calculated
Elo first turns the rating gap between two players into an expected score using a logistic curve on a 400-point scale. The actual result is then compared with that expected score, and the difference — scaled by the K-factor — is the rating change the result produces.
- R_A
- player A's rating before the game
- R_B
- player B's rating before the game
- E_A
- player A's expected score — an internal weighting of the rating system, between 0 and 1, not a match forecast
- S_A
- player A's actual score: 1 for a win, 0.5 for a draw, 0 for a loss
- K
- the K-factor, how much a single result moves the rating
- R'_A
- player A's updated rating after the game
Because every point A gains is a point B loses (the expected scores sum to 1 and K is shared),
the update is zero-sum: R'_B = R_B + K × (S_B − E_B) moves the same magnitude in
the opposite direction.
Worked example: 1600 beats 1400, K = 32
Player A is rated 1600, player B 1400, and A wins, so S_A = 1.
- Expected score:
E_A = 1 / (1 + 10^((1400 − 1600) / 400)) = 0.76 - Player B's expected score:
E_B = 1 − 0.76 = 0.24 - Rating change:
32 × (1 − 0.76) = +8points to A - Updated ratings:
A = 1608,B = 1392
Read the 0.76 as “the system already expected A to take most of the points here, so winning adds only a little.” It is the rating change this result produces, not a claim that A had a 76% chance of winning.
Rating gap and expected score (reference)
For any rating gap, the higher-rated player's expected score comes straight from the formula. These values are fixed by the 400-point scale and do not depend on the K-factor.
| Rating gap | Expected score (higher-rated) |
|---|---|
| 0 | 0.50 |
| 50 | 0.57 |
| 100 | 0.64 |
| 200 | 0.76 |
| 400 | 0.91 |
| 800 | 0.99 |
Accuracy notes and limits
Elo assumes a fixed logistic relationship between rating gaps and results, and a single K-factor. Different bodies and leagues pick different K values and starting ratings, so ratings are only comparable within one system — a 1600 in one pool is not a 1600 in another. The expected score says nothing about form, injuries, surface or conditions, and it is not a betting probability or an outcome predictor. Treat it as how the rating system weights a result, and see our editorial policy.
Frequently asked questions
Is the expected score the chance of winning?
No. It is an internal weighting the rating system uses to decide how many points a result should move. It is calibrated to long-run results within one rating pool, not a forecast of a specific match.
Why do some systems use different K-factors?
K controls responsiveness. New players or fast-moving pools use higher K so ratings settle quickly; established players use lower K for stability. Because K differs between bodies, the points exchanged for the same result can differ too.
Do the two players always exchange the same points?
Yes. The expected scores sum to 1 and the K-factor is shared, so whatever one player gains the other loses. The system is zero-sum for a single game between two players.
Related tools and reading
Racquet & scoring guides
How rating and scoring systems work across racquet and head-to-head sports.
Sources
- Elo, A. (1978). The Rating of Chess Players, Past and Present — the logistic expected-score model and the rating update rule.