Calculate your new Elo rating after any game. Enter your rating, your opponent's rating, and the result to get expected score, rating change, performance rating, and percentile.
Game Game Details
This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
New Rating
1500
Enter a game result above to calculate
Expected Score
0.500
Rating Change
+20
New Rating
1520
Perf. Rating
1900
K-Factor
40
Percentile
~50th
E = 1/(1+10^((Opp-My)/400))
ΔR = K × (S − E)
The expected score E ranges from 0 (certain loss) to 1 (certain win), with 0.5 at equal ratings. The S-curve below shows how your expected score changes as the rating gap widens. Values update automatically from Tab 1.
Rating Difference (Your rating - Opponent's)
0
Expected Score
0.500
Score %
50.0%
Assessment
Even Match
Rating Diff (My−Opp)
Expected Score
Score %
Assessment
Simulate a series of games and track your rating trajectory. Add each game result to see how your rating evolves across a session or tournament.
+ Add Game
Syncs with Calculator tab. Changing it resets all games.
E is an expected game score, not a uniquely determined win probability when draws are possible.
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Walk-through
How to Use This Calculator
4 steps▸
1
Enter Player Ratings and Result
Input your current Elo rating and your opponent's Elo rating. Select the game result: Win, Draw, or Loss. The calculator computes the expected score (your win probability based on the rating difference) and the rating change for each outcome.
2
Select or Auto-Detect the K-Factor
This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
3
Review the Rating Change
The hero display shows your new rating and the change (ΔR = K × (S − E), where S is your score and E is your expected score). Stat cards show the expected score probability, performance rating for this game, and your estimated percentile in the rated player population.
4
Track a Tournament in the Tournament Simulator
Switch to the Tournament tab to simulate a full tournament rating path. Enter a starting rating, add game results one by one (each with an opponent's rating), and track cumulative rating changes, win/loss/draw record, and final rating across the full event.
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Reference
Formula & Methodology
3 formulas▸
Expected Score
E = 1 / (1 + 10^((R_opp − R_me) / 400))
E is an expected game score, not a uniquely determined win probability when draws are possible. A win scores 1, a draw 0.5 and a loss 0. The page uses an uncapped logistic difference divided by 400; official FIDE table probabilities and rating-period rules are not applied.
Rating Change
ΔR = K × (S − E) · R_new = R_old + ΔR
This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
The single-game performance rating estimates the rating that would be consistent with the game result against this opponent. Beating a 1500-rated player implies a performance of 1900; drawing implies 1500; losing implies 1100. This approximation follows from the expected-score formula: if your performance rating exactly matched R_opp ± 400, you would have expected score 0.909 or 0.091. Over a multi-game tournament, performance rating is averaged across all games.
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Glossary
Key Terms Explained
6 terms▸
Elo Rating ↗A numerical system for rating the relative skill of players in zero-sum games, developed by physicist Arpad Elo in the 1960s for chess. The expected score formula E = 1/(1+10^(ΔR/400)) maps rating differences to win probabilities using a logistic function. Ratings are updated after each game based on the difference between actual and expected score. Elo is used in chess, Go, checkers, and has been adapted to team sports (FIFA world rankings), video games (online multiplayer matchmaking), and academic peer review.
K-Factor ↗This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
Expected Score (E) ↗The probability-weighted expected outcome of a game based on the rating difference: E = 1/(1+10^((R_opp−R)/400)). E ranges from 0 (certain loss) to 1 (certain win). E = 0.5 when ratings are equal. E = 0.909 when the player is rated 400 points above the opponent. E is a probability in a single game, but is also interpreted as the expected fraction of points in a multi-game match.
FIDE Rating ↗This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
Performance Rating ↗A retroactive estimate of the rating a player performed at during a specific event or game. Computed by solving for the rating that would have given an expected score equal to the actual result. Over a tournament, performance rating = average opponent rating + 400 × (wins − losses) / games. It measures how well the player actually played, independent of their starting rating.
Rating Deflation/Inflation ↗The phenomenon where average Elo ratings in a pool trend lower (deflation) or higher (inflation) over time. Deflation occurs when new players enter the pool at an inflated rating, then their rating drops as the pool absorbs the points. Inflation occurs when strong players retire with high ratings they no longer earn. FIDE and major platforms periodically recalibrate initial ratings and K-factors to counteract drift.
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Scenarios
Real-World Examples
2 worked examples▸
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Upset Win: Low-Rated vs. High-Rated
Rating Upset
My Rating 1200Opponent Rating 1800Result WinK-Factor 40 (auto, <2100)
E = 1/(1+10^((1800−1200)/400)) = 1/(1+10^1.5) = 1/(1+31.62) = 0.0307. S = 1 (win). ΔR = 40×(1−0.0307) = 40×0.969 = +38.8 ≈ +39 points. New rating: 1200 + 39 = 1239. A 600-point rating difference gives only a 3% win probability — making this a huge upset. The winner gains nearly a full K (39/40 = 97.5% of max), while the opponent loses the same 39 points. Performance rating for this game ≈ 1800 + 400 = 2200. This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
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Equal Opponents: Draw
Equal Match
My Rating 1500Opponent Rating 1500Result DrawK-Factor 40 (auto)
E = 1/(1+10^0) = 1/2 = 0.500. S = 0.5 (draw). ΔR = 40×(0.5−0.5) = 0. Rating unchanged. When ratings are equal, the expected score is exactly 0.5 and a draw produces no rating change for either player — the most fair outcome. A win would yield +20 points; a loss −20 points. Equal-rated players in a 100-game series would see their ratings converge to their true skill level as wins and losses balance out. This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
APA
MLA
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Deep Dive
Elo Rating: How Chess Rankings Work and Why the System Is Used Everywhere
E is an expected game score, not a uniquely determined win probability when draws are possible. A win scores 1, a draw 0.5 and a loss 0. The page uses an uncapped logistic difference divided by 400; official FIDE table probabilities and rating-period rules are not applied. This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
The Mathematics of Expected Score
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E is an expected game score, not a uniquely determined win probability when draws are possible. A win scores 1, a draw 0.5 and a loss 0. The page uses an uncapped logistic difference divided by 400; official FIDE table probabilities and rating-period rules are not applied.
K-Factor: Stability vs. Responsiveness
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This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
Elo Beyond Chess: Team Sports and Online Games
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Elo's elegance — requiring only win/draw/loss outcomes and current ratings — made it ideal for adoption beyond chess. FIFA uses an Elo-variant for national team rankings that assigns match weights by tournament importance and adjusts for goal difference. The NFL has used Elo-based power ratings for forecasting since the 1980s, and FiveThirtyEight's NFL Elo model achieved notable prediction accuracy. Video game multiplayer matchmaking systems in League of Legends, Dota 2, and most competitive games use Elo or TrueSkill (a Bayesian extension that handles team games and accounts for uncertainty). The key insight that made Elo extensible: any zero-sum game with binary outcomes (win/loss) or ordered outcomes (win/draw/loss) can be modeled with the same expected-score framework, with the K-factor and scale constant tuned to the specific game's competitive environment. The main limitation of classic Elo for team sports is that it treats teams as single players — individual performance variance is averaged out, and roster changes require manual adjustment.
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Questions
Frequently Asked Questions
6 questions▸
What is the Elo rating system?+
A method for calculating the relative skill of players in zero-sum games, developed by Arpad Elo for chess in the 1960s. Each player has a numerical rating; after each game, ratings are updated based on the difference between actual score (1=win, 0.5=draw, 0=loss) and expected score (derived from the rating difference). Higher ratings = stronger players. FIDE Grandmasters typically hold ratings of 2500+.
How is the expected score calculated in Elo?+
E = 1 / (1 + 10^((R_opp − R_me) / 400)). At equal ratings: E = 0.5 (50/50). At 200-point advantage: E ≈ 0.76. At 400-point advantage: E ≈ 0.91. At 600-point advantage: E ≈ 0.97. The expected score is your probability of winning the game.
What is the K-factor and how does it affect rating changes?+
This is an illustrative logistic Elo model. Auto uses K=40 below 2100, K=20 below 2400 and K=10 otherwise. It does not implement official FIDE player-history K rules, probability tables, standard/rapid scope, rating-period rounding or the 400-point cap. Tournament steps are sequential examples, not an official rating-period update.
How much do I gain or lose for beating a higher-rated player?+
ΔR = K × (1 − E). If you're rated 1200 and beat a 1800-rated player: E ≈ 0.031, ΔR = 40 × (1 − 0.031) = +38.8 points. The bigger the upset (lower E), the more points you gain. Losing to a much lower-rated player: ΔR = K × (0 − E) = −K × E, which is large and negative.
What Elo rating is considered good in chess?+
Approximate FIDE levels: Beginner: 400–800. Novice: 800–1200. Class B: 1400–1600. Class A: 1600–1800. Expert: 1800–2000. National Master: ~2000–2200. FIDE Master: 2300+. International Master: 2400+. Grandmaster: 2500+. World Champion: 2800+. Average club player is approximately 1400–1600. Online ratings (Chess.com, Lichess) are typically 200–400 points higher than FIDE ratings due to different player pools and K-factor settings.
Is Elo used in sports other than chess?+
Yes. FIFA uses an Elo-variant for national team rankings. NFL, NBA, and MLB sabermetric sites use Elo-based power ratings for win probability models. Online multiplayer games (League of Legends, Dota 2, Starcraft) use Elo or Elo-derived systems (Microsoft TrueSkill) for matchmaking. Even academic paper and grant review systems have used Elo for ranking competing proposals.
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