Elo Rating Calculator
Calculate new Elo ratings after a match for chess, gaming, and competitive ranking systems. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
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%)\nExpected score for 1600: 0.7597 (76%)\nThe 1400 player won (actual = 1):\nRating change = 20 × (1 - 0.2403) = +15.2 → +15\nNew rating for 1400: 1415\nNew 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%)\nDraw (actual = 0.5):\nRating change = 32 × (0.5 - 0.5) = 0\nBoth ratings unchanged at 1500\nDraws 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.
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).
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy