Elo Rating Calculator

The Elo rating system, developed by physicist Arpad Elo in the 1960s, is a method for calculating the relative skill levels of players in competitive games. It is used in chess, video games, sports leagues, and many online platforms.

Expected score formula: Expected Score (A) = 1 ÷ (1 + 10^((Rating_B − Rating_A) / 400))

Read that as average points per game, not as a win percentage. A win is worth 1, a draw 0.5, a loss 0, so an expected score of 0.60 means “on average, six points from ten games”. It is easy to misread as a 60% chance of winning, and in chess that reading is badly wrong: draws are common at every level and above master level they are the most likely single result, so a player expected to score 0.60 might win 40% and draw 40% rather than win 60%. In a game with no draws at all the two readings do coincide, which is why the shorthand survives in video-game matchmaking.

Rating update formula: New Rating = Old Rating + K × (Actual Score − Expected Score)

Where:

• Actual Score: 1 for win, 0.5 for draw, 0 for loss
• K-factor: controls how quickly ratings change

K-factor values in chess (FIDE, the Fédération Internationale des Échecs, is the world chess federation):

• K = 40 for new players (first 30 rated games)
• K = 20 for established players (under 2400)
• K = 10 once a player has reached 2400, even if they later drop below it

The USCF (United States Chess Federation) uses a different scale, with K near 32 for most club-level ratings. Pick the one your league actually uses, because the same result can move you twice as far under one as under the other.

Worked example: Player A (rated 1500) beats Player B (rated 1700). Expected Score (A) = 1 ÷ (1 + 10^((1700−1500)/400)) = 1 ÷ (1 + 10^0.5) = 1 ÷ 4.162 = 0.240

Rating Change (A) = 20 × (1 − 0.240) = 20 × 0.760 = +15.2 points New Rating (A) = 1500 + 15 = 1515 New Rating (B) = 1700 − 15 = 1685

Rating benchmarks (chess):

• Below 1000: beginner
• 1000–1400: intermediate club player
• 1400–1800: strong club player
• 1800–2200: expert
• 2200–2300: Candidate Master (CM)
• 2300–2400: FIDE Master (FM)
• 2400–2500: International Master (IM)
• 2500 and up: Grandmaster (GM)

Magnus Carlsen’s peak of 2882, set in May 2014, is still the highest rating anyone has held. For context on how slowly the top moves: that record has stood for over a decade, while a club player can swing 200 points in a single busy season.