Elo Rating Calculator
Calculate Elo rating changes after a match. Enter player ratings, K-factor, and game result to see new ratings, expected scores, and win probabilities.
Elo Rating Calculator
Calculator
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Formula: New Rating = Old Rating + K × (Actual Score - Expected Score)
Worked example — Player 1: 1400 → 1415 (+15) | Player 2: 1600 → 1585 (-15)
Formula
New Rating = Old Rating + K × (Actual Score - Expected Score)
Expected Score = 1 / (1 + 10^((Opponent Rating - Player Rating) / 400)). After a game, the rating changes by K × (Actual - Expected). Actual score is 1 for a win, 0.5 for a draw, and 0 for a loss. K-factor controls the maximum possible rating change per game.
Worked Examples
Example 1: Upset Victory
Problem:A 1400-rated player beats a 1600-rated player. K-factor = 20.
Solution:Expected score for 1400: 1/(1+10^(200/400)) = 0.2403 (24%) Expected score for 1600: 0.7597 (76%) The 1400 player won (actual = 1): Rating change = 20 × (1 - 0.2403) = +15.2 → +15 New rating for 1400: 1415 New rating for 1600: 1600 + 20 × (0 - 0.7597) = 1585
Result:Player 1: 1400 → 1415 (+15) | Player 2: 1600 → 1585 (-15)
Example 2: Expected Result Between Equal Players
Problem:Two 1500-rated players draw. K-factor = 32.
Solution:Expected score for both: 0.5000 (50%) Draw (actual = 0.5): Rating change = 32 × (0.5 - 0.5) = 0 Both ratings unchanged at 1500 Draws between equal players result in no rating change
Result:Both players: 1500 → 1500 (no change)
Frequently Asked Questions
What is the Elo rating system?
The Elo rating system, invented by Arpad Elo in 1960, is a method for calculating the relative skill levels of players in zero-sum games like chess. Each player has a numerical rating, and the system predicts the probability of one player beating another based on their rating difference. After a game, ratings are adjusted — winners gain points and losers lose points. The amount gained or lost depends on the expected outcome: beating a much higher-rated player earns more points than beating a lower-rated one. The system is used in chess (FIDE), online gaming, sports, and even competitive programming.
How does the expected score formula work?
The expected score uses the logistic function: E = 1 / (1 + 10^((Rb - Ra)/400)). This means a 200-point rating advantage gives approximately a 76% expected win rate, a 400-point advantage gives ~91%, and equal ratings give 50%. The 400 in the denominator is a scaling factor that determines how many rating points equal a tenfold difference in winning probability. When two players are 400 points apart, the higher-rated player is expected to score 10 times the lower-rated player's score over many games.
What is the K-factor and how does it affect ratings?
The K-factor determines how much ratings can change from a single game. A higher K-factor means larger swings. FIDE chess uses: K=40 for new players (first 30 games), K=20 for most players, and K=10 for players rated above 2400. Online platforms like Chess.com use K=32 for provisional ratings. A higher K-factor makes the system more responsive to recent results but also more volatile. New players need high K-factors to quickly reach their true rating. Established players need low K-factors for stability.
What does my Elo rating number mean?
In chess: Below 1000 = Beginner, 1000-1200 = Novice, 1200-1400 = Intermediate, 1400-1600 = Club player, 1600-1800 = Strong club player, 1800-2000 = Expert/Candidate Master, 2000-2200 = National Master, 2200-2400 = International Master, 2400-2500 = Grandmaster, 2500-2700 = Super GM, 2700+ = World elite (top ~50 players). The average casual player is around 800-1000. The average club player is around 1400-1600. Magnus Carlsen's peak was 2882. In other games, the scale may differ but the relative comparison principle remains the same.
Can Elo ratings be used outside of chess?
Absolutely! Elo ratings are used in many competitive environments. Online gaming: League of Legends, Dota 2, and Overwatch use Elo-based systems. Sports: FIFA uses Elo for national team rankings. Tennis uses a similar system. Competitive programming: Codeforces and TopCoder use Elo variants. Education: some adaptive learning platforms rate student skill levels. Dating apps: Tinder originally used an Elo-like system to rank profiles. The system works for any activity where two parties compete and there's a winner and loser (or draw).
How does Elo differ from Glicko and TrueSkill?
Elo stores a single number per player and assumes the uncertainty around it is the same for everyone, which is why the K-factor has to be tuned by hand for newcomers. Glicko adds a ratings deviation that tracks how confident the system is in each rating and widens again during inactivity, so an uncertain player's rating moves faster automatically. TrueSkill extends the same idea to teams and multiplayer free-for-alls by modelling each player as a distribution and updating both its mean and its spread. All three predict outcomes from a rating difference; the newer systems mainly manage uncertainty better.
Is the Elo system zero-sum, and what causes rating inflation?
Within a single game the points one player gains are exactly the points the other loses, provided both use the same K-factor, so the pool total is conserved. Inflation or deflation arises at the edges of the pool: new players entering with a fixed provisional rating inject or remove points, improving juniors carry points upward as they leave the beginner pool, and rating floors prevent points from draining out at the bottom. Because of this, a rating of 1800 in one federation or platform is not directly comparable to 1800 in another.
How are new players given a starting rating?
Most systems seed an unrated player with a provisional rating and a high K-factor so that early results move the number quickly toward its true level. FIDE, for example, uses K=40 for a player's first games. Some pools instead compute an initial rating from a set of calibration games as the average opponent rating adjusted by the score achieved, then switch to normal updates. The purpose in every case is the same: converge fast while the estimate is uncertain, then slow down for stability.
What is a performance rating and how is it different from your actual rating?
A performance rating estimates the strength implied by one event's results, ignoring your prior rating entirely. The common linear approximation is the average opponent rating plus 400 times (wins minus losses) divided by the number of games. Scoring 4 out of 6 against opponents averaging 1900 gives 1900 plus 400 times 2 divided by 6, roughly 2033. Your published rating is instead a running estimate updated game by game, so a single strong performance moves it only by the K-weighted amount rather than jumping to the performance figure.
Why do draws still change your rating?
A draw scores 0.5, and the update compares that against your expected score, so the outcome only leaves your rating unchanged when the expectation is exactly 0.5, meaning the two players were equally rated. Drawing a much stronger opponent gains points because the expectation was below 0.5, while drawing a much weaker one loses points for the same reason in reverse. This is why draw-heavy formats still separate players over time, and why avoiding strong opposition is not a route to a higher rating.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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