Elo Rating Calculator
How an Elo rating changes after a game — with the expected score the ratings predicted, and the new ratings for both players.
Elo, invented by Arpad Elo for chess and now used from football to video games, works on one idea: the rating gap predicts the result.
How the elo rating calculator works
Elo, invented by Arpad Elo for chess and now used from football to video games, works on one idea: the rating gap predicts the result. A 400-point gap means the stronger player is expected to score ten times as often as the weaker. The expected score is 1 ÷ (1 + 10^((opponent − player) ÷ 400)), and the rating moves by K × (actual − expected).
K controls how fast ratings move. Chess uses 40 for newcomers, 20 for most players and 10 for masters, so an established rating is stable while a new one finds its level quickly. The elegance is that beating a much stronger opponent gains a great deal and beating a much weaker one gains almost nothing — the rating already predicted it.
Formula: expected = 1 ÷ (1 + 10^((Rb − Ra) ÷ 400)); new = Ra + K × (score − expected)
Worked examples
| Inputs | Rating change | Note |
|---|---|---|
| Beating a 1750 as a 1600 | 14.1 | expected 29.5%, so a win gains 14.1 |
| Losing to a much weaker player | -18.2 | costs 18.2 — the rating expected a win |
| A draw between equals | 0 | no change |
FAQFrequently asked questions
How does Elo work?
The rating gap predicts the result. You gain K × (what you scored − what was expected), so beating a stronger player gains more than beating a weaker one.
What does a 400-point gap mean?
The stronger player is expected to score about 91% — roughly ten times as often as the weaker one.
What is the K-factor?
How fast ratings move. Chess uses 40 for newcomers, 20 for most players and 10 for masters, so established ratings are stable.
Is Elo zero-sum?
Yes in the classic form — the points one player gains, the other loses. Some implementations add adjustments that break this.
Where else is Elo used?
Football rankings, tennis, board games and video-game matchmaking. The underlying formula is unchanged from Elo's chess work.
Where these figures come from
- World Handicap System — Rules of Handicapping — the score differential and handicap index formula
- International Cricket Council — Playing Conditions — over structure and run-rate definitions
- Cricket Australia — the national body for the sport these statistics most often describe here
Last checked: September 2026. Formulas follow the governing bodies where one publishes them — the World Handicap System for golf, the ICC playing conditions for cricket run rates.