Elo Rating Calculator
The Elo rating system calculates updated ratings after each match using the formula R' = R + K(S - E), where K is the sensitivity factor and E is the expected outcome based on the rating difference. Originally developed by physicist Arpad Elo for chess (adopted by FIDE in 1970), the Elo system is now used across sports analytics, esports, and competitive ranking systems worldwide. Enter both players' ratings, the K-factor, and the match result to calculate updated ratings.
Elo rating formula
E(A) = 1 / (1 + 10^((Rb - Ra) / 400))
R'(A) = Ra + K × (S - E(A))
R'(B) = Rb + K × ((1 - S) - (1 - E(A)))
Where Ra and Rb are current ratings, K is the K-factor, S is 1 (win), 0.5 (draw), or 0 (loss) for player A, and E(A) is the expected probability of player A winning based on the rating difference.
Elo rating scale reference
- FIDE Chess Grandmaster: typically above 2500.
- International Master: typically 2400 to 2500.
- Typical strong amateur: 1600 to 1800.
- Beginner/casual player: below 1200.
- FiveThirtyEight uses Elo for NFL/NBA with starting rating around 1500.
Elo rating: frequently asked questions
What is the Elo rating system?
The Elo rating system is a method for calculating the relative skill levels of players or teams in zero-sum games. It was originally developed by Arpad Elo for chess ratings and is now used in chess, sports analytics, video games, and competitive rankings worldwide.
What is the Elo formula?
The new rating is R' = R + K x (S - E), where R is the current rating, K is the K-factor (controls how much ratings change per game), S is the actual score (1 for win, 0.5 for draw, 0 for loss), and E is the expected score: E = 1 / (1 + 10^((opponent rating - own rating) / 400)).
What is the K-factor in Elo?
The K-factor determines how much a single game affects ratings. A higher K causes larger swings per game. FIDE (chess) uses K=40 for new players, K=20 for established players below 2400, and K=10 for players above 2400. Sports analytics often use K=20 or K=32.
What is the expected score in Elo?
The expected score E = 1 / (1 + 10^((Rb - Ra) / 400)) for player A, where Ra and Rb are the ratings. If player A has rating 1600 and player B has 1400, player A's expected score is approximately 0.76 (76% expected win probability).
What does a 400-point Elo difference mean?
A 400-point rating difference gives the higher-rated player an approximately 91% expected probability of winning each game. In chess, a 200-point difference gives approximately a 76% win probability. The 400 constant in the formula is a design choice by Elo that makes the ratings interpretable.
Official sources
- FIDE Rating Regulations: fide.com/fide/handbook.html.
- United States Chess Federation Rating System: uschess.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.