Elo Rating Calculator (Expected Score & New Ratings)
Enter both players' ratings, the K factor and the result for player A to see the win probability and the rating change for both players. Use it to see how many points you gain for beating a stronger player, or what win probability a rating gap means.
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Formula
Expected score of A: E_A = 1 / (1 + 10^((R_B - R_A) / 400)), andE_B = 1 - E_ANew rating = old rating + K x (S - E), where S is 1 for a win, 0.5 for a draw and 0 for a loss
Worked example
Player A is rated 1600 and player B 1400, with K = 32.
- E_A = 1 / (1 + 10^-0.5) = 0.7597, so A is expected to score 75.97%.
- If A wins: change = 32 x (1 - 0.7597) = +7.69, giving 1607.69 for A and 1392.31 for B.
- If A loses: change = 32 x (0 - 0.7597) = -24.31.
- If they draw: change = 32 x (0.5 - 0.7597) = -8.31.
The same K is applied to both players here. Elo is a model: it is an estimate of strength, and different organisations use different K factors.
When to use it
Use it for chess, esports, table tennis, league ladders or any head-to-head game where you keep ratings. It works out the expected result before the game and the new ratings after it.
Typical values (rules of thumb)
- A 400 point gap means the stronger player is expected to score about 91% (10 to 1 odds).
- Equal ratings give 50%, and a 200 point gap gives about 76%.
- K = 32 is a common default for casual systems. Chess federations use smaller values for established players, for example FIDE uses 10, 20 or 40 depending on rating and experience.
Common mistakes
- Forgetting that the rating change is symmetric here: what A gains, B loses.
- Using a large K on established players, which makes ratings jump around.
- Treating the expected score as a pure win chance. A draw counts as half a point, so it is an expected score.
How it differs from nearby tools
The win percentage calculator and the Pythagorean expectation calculator summarise a season record. Elo is updated game by game and measures strength relative to opponents.
Frequently asked questions
What is the Elo expected score formula?
E = 1 / (1 + 10^((Rb - Ra)/400)). A player rated 1600 against a 1400 player has E = 1 / (1 + 10^-0.5) = 0.76, so 76% of a point is expected per game. The two expected scores always add up to 1.
How are the new Elo ratings calculated?
New rating = old rating + K x (actual score - expected score), where the score is 1 for a win, 0.5 for a draw and 0 for a loss. With K = 32, the 1600 player winning gains 32 x (1 - 0.76) = 7.7 points and the loser drops by the same amount.
What K factor should I use?
K sets how fast ratings move. FIDE chess uses 40 for new players (first 30 games), 20 for players under 2400 and 10 once a player has reached 2400. Many online games use 16 to 32. A higher K reacts faster but is noisier.
Is the rating change the same for both players?
Yes, when both players use the same K factor the points one player gains are exactly what the other loses. If the players use different K factors, each rating moves by its own K, so enter the K for each player separately.
How many Elo points do you gain for a win?
With K = 32, beating an equally rated opponent gains 16 points. Beating a player rated 200 points higher gains 24.31, because the win was less expected: 32 x (1 - 0.2403) = 24.31.
What is the Elo win probability for a 400 point rating difference?
The expected score is 1 / (1 + 10^(-400/400)) = 0.909, so the higher rated player is expected to score about 91%. A 200 point gap gives about 76%.
What happens to Elo ratings after a draw?
A draw counts as half a point for each player. If a 1600 player draws with a 1400 player (K = 32), the favourite loses 32 x (0.5 - 0.7597) = 8.31 points and ends on 1591.69, while the underdog gains 8.31.