What is the Elo expected-score formula?

Expected score E equals 1 divided by (1 + 10 raised to the power of (opponent rating minus your rating) divided by 400). It estimates the fraction of a point you should average against that opponent.

How is the new rating calculated?

New rating equals your current rating plus K times (actual score minus expected score), where actual score is 1 for a win, 0.5 for a draw, and 0 for a loss. K scales how much a single game moves your rating.

Which K-factor should I use?

FIDE uses K of 40 for new players with fewer than 30 rated games, 20 for players rated under 2400, and 10 for masters rated 2400 or above. Online sites may use different values, so match your federation or platform.

Why did I gain points for a draw?

If your opponent is rated higher than you, your expected score is below 0.5, so even a draw beats expectation and earns rating points. Against a lower-rated opponent the same draw loses points.

Does this match official FIDE ratings exactly?

It uses the same per-game formula FIDE applies. Official ratings are published periodically and combine all of your games in a rating period, but each game's contribution follows this exact calculation.

Chess Elo Rating Calculator

The Chess Elo Rating Calculator shows what a single game does to your rating. Feed it your rating, your opponent’s rating, the result, and your K-factor, and it returns your new rating plus the expected score — the same math FIDE and most online platforms use under the hood.

How it works

Elo is built on one idea: the rating gap between two players predicts the result. Your expected score is

E = 1 / (1 + 10^((Rᵦ − Rₐ) / 400))

where Rₐ is your rating and Rᵦ is your opponent’s. A 0 means certain loss, 1 means certain win, and 0.5 is an even match. The divisor of 400 means a 400-point gap makes the favourite roughly ten times more likely to win.

After the game your rating updates by

R’ = Rₐ + K × (S − E)

where S is your actual score (1 win, 0.5 draw, 0 loss) and K is the development coefficient. Outperforming your expected score gains points; underperforming loses them.

Choosing a K-factor

FIDE uses K = 40 for newcomers (under 30 rated games), K = 20 for players rated below 2400, and K = 10 for masters at 2400 and above. A larger K moves your rating faster, which is why new players climb or fall quickly while established masters change slowly.

Example and notes

Suppose you are rated 1500 and beat a 1600-rated opponent with K = 20. Your expected score is about 0.36, so you gain roughly 20 × (1 − 0.36) ≈ 13 points. Lose to that same opponent and you drop only about 7 points, because the result was the more likely outcome. The asymmetry is what makes upsets rewarding.