Elo Rating Calculator
See your new Elo rating after a game: the expected score from the rating gap, the points won or lost, and how the K-factor scales it.
How it works
Expected E = 1 ÷ (1 + 10^((opponent − you) ÷ 400)) · New rating = you + K × (score − E), where score is 1 win, 0.5 draw, 0 loss
The Elo system, built for chess and now used across games and sports, turns a rating gap into a win probability. A 400-point lead corresponds to a 10-to-1 expected score, and equal ratings give a coin-flip 50%. After a game you gain or lose points equal to the K-factor times the difference between what you actually scored and what was expected — so beating a much stronger opponent (a large surprise) earns far more than beating a weaker one. The K-factor sets how twitchy ratings are: a low K (around 16) suits established masters whose rating should barely move, while a high K (around 40) lets new or provisional players climb to their true level quickly.
Worked example
You are rated 1500 and beat an opponent rated 1600. Your expected score is 1 ÷ (1 + 10^((1600 − 1500) ÷ 400)) = 1 ÷ (1 + 10^0.25) ≈ 0.36. With a K-factor of 32, the change is 32 × (1 − 0.36) ≈ +20.5, lifting you to about 1520 — a big gain because you were the underdog.
Frequently asked questions
What does the K-factor do?
It sets how many points a single game can move your rating. A high K (40) makes ratings swing fast, useful for new players finding their level; a low K (16) keeps established ratings stable. Many club systems use 32.
Why do I gain more for beating a higher-rated player?
Elo rewards surprises. Your expected score against a stronger opponent is low, so an unexpected win produces a large "score minus expected" gap — and therefore a bigger rating gain. Beating someone far weaker was expected, so it earns very little.
What does the expected score percentage mean?
It is the share of a point you would average against that opponent over many games — effectively your win probability once draws are counted as half. A 36% expected score means you would win a bit over a third of the time.
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This calculator is for educational purposes. Double-check important results before acting on them.