Calculate Elo rating, K-factor, actual score, or expected score from the other four values using the standard Elo formula and steps.
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Elo Rating Formula
The Elo rating update is based on the difference between the actual score and the expected score. A result better than expected increases the rating, and a result worse than expected decreases it.
NewR = OldR + K*(S - E)
- NewR = new Elo rating after the game or match
- OldR = Elo rating before the game or match
- K = K-factor, which controls how much the rating can change
- S = actual score, usually 1 for a win, 0.5 for a draw, and 0 for a loss
- E = expected score, usually a value between 0 and 1
The calculator can solve for any one missing value when the other four values are entered.
OldR = NewR - K*(S - E)
Use this rearranged formula when you know the new rating and want to find the old rating.
K = (NewR - OldR)/(S - E)
Use this formula to find the K-factor. This only works when the actual score is not equal to the expected score.
S = ((NewR - OldR)/K) + E
Use this formula to find the actual score implied by a rating change.
E = S - ((NewR - OldR)/K)
Use this formula to find the expected score implied by a rating change.
Common Elo Score and K-Factor Values
Actual score is usually entered as 1, 0.5, or 0 for a single game. K-factor depends on the rating system being used.
| Game result | Actual score | Meaning |
|---|---|---|
| Win | 1 | You scored the full point. |
| Draw | 0.5 | You scored half a point. |
| Loss | 0 | You scored no points. |
| K-factor | Typical use | Effect on rating change |
|---|---|---|
| 10 | Stable or high-level ratings | Small changes after each result |
| 20 | General rating updates | Moderate changes |
| 40 | New or provisional players | Larger changes after each result |
Example Elo Rating Calculations
Example 1: Calculate a new Elo rating after a win
You have an old rating of 1500, a K-factor of 20, an actual score of 1, and an expected score of 0.6.
NewR = 1500 + 20*(1 - 0.6)
NewR = 1500 + 8 = 1508
The new Elo rating is 1508.
Example 2: Calculate a new Elo rating after a loss
You have an old rating of 1800, a K-factor of 10, an actual score of 0, and an expected score of 0.75.
NewR = 1800 + 10*(0 - 0.75)
NewR = 1800 - 7.5 = 1792.5
The new Elo rating is 1792.5.
FAQ
What is expected score in Elo?
Expected score is the result you are predicted to get before the game. It is usually between 0 and 1. An expected score of 0.75 means you are expected to score 75% of the available point. If your actual score is higher than your expected score, your rating goes up. If it is lower, your rating goes down.
What K-factor should you use?
Use the K-factor required by the rating system you are following. If you are making a general estimate, 20 is a common middle value. A lower K-factor makes ratings change slowly, while a higher K-factor makes ratings respond more quickly to wins and losses.
Can Elo rating changes be decimal values?
Yes. The formula can produce decimal rating changes, especially when the expected score is a decimal. Some rating systems keep decimals internally, while others round the final rating to a whole number.
