Chess Elo Calculator
Compute expected score and rating change after a chess game.
Overview
The Chess Elo Calculator computes the expected score and the post-game rating change for a single chess game between two rated players. Enter your rating, your opponent's rating, your result (win, loss, or draw), and your K-factor, and the calculator returns the rating delta that FIDE, USCF, and most online chess servers apply.
Elo is the foundational rating system in chess and is also widely used in other competitive games. It models each player's strength as a single number and predicts a probability distribution over outcomes based purely on the rating gap. The calculator shows the prediction first so you can see whether the game was an upset, then the rating change that brings the model back in line with reality.
How it works
The expected score E for player A against player B is E = 1 / (1 + 10^((Rb - Ra)/400)). A 400-point gap predicts the higher-rated player to score about 91 percent — usually as wins and draws combined. Equal ratings give E = 0.5 for both sides.
After the game, the rating change for player A is K * (S - E), where S is the actual score (1 for a win, 0.5 for a draw, 0 for a loss) and K is the volatility coefficient. K = 40 is common for fresh players or rapid pools, K = 20 for established standard ratings, and K = 10 for elite players whose ratings shouldn't swing on a single result. The model is zero-sum at fixed K: whatever one player gains, the other loses.
Examples
- A 1500 player beats a 1500 player at K = 20. Expected score 0.5, actual 1, change = 20 * (1 - 0.5) = +10. Loser loses 10.
- A 2000 player beats a 1600 player at K = 20. Expected score 0.91, actual 1, change = 20 * (1 - 0.91) = +1.8. Loss for the 1600 if they had won would have been +8.0.
- A 1200 draws a 1400 player at K = 40. Expected score 0.24, actual 0.5, change = 40 * 0.26 = +10.4 for the 1200.
- A 2700 elite player draws a 2400 at K = 10. Expected 0.85, actual 0.5, change = 10 * (-0.35) = -3.5.
FAQ
What K-factor should I use?
Most platforms use 40 for new players, 20 for the rated pool, and 10 for top players. Check the platform's published rule.
Why doesn't a draw between equal players change ratings?
Because the expected score is already 0.5 — the actual matches the prediction, so no update is needed.
Can ratings go below zero?
In principle no, but most pools floor ratings at 100 or 200 to avoid degenerate cases.
Does Elo handle three-player games?
The classic formula is two-player. Multiplayer extensions exist (Glicko, TrueSkill) but aren't standard chess.
How does this differ from Glicko?
Glicko tracks rating deviation (uncertainty) alongside the rating, so changes shrink as your rating stabilises.