Elo Rating Calculator (Chess and Game Rating Change)
Your expected score against an opponent, and your new rating after a win, draw or loss, using the Elo system with a K-factor of your choice.
Results
The dashed line marks the value you entered.
What this tool does
Arpad Elo's system assumes performance follows a logistic curve in which a 400-point gap makes the stronger player ten times as likely to win as to lose, so a player 200 points up is expected to score about 76 %. After the game the rating moves by K times the difference between the actual and the expected score: beating a stronger player gains more than beating a weaker one. K is set by each federation, commonly 10 to 40, higher for new or young players. A draw counts as half a point.
Formula
E = 1 ÷ (1 + 10^((R_B − R_A) ÷ 400)) · new rating = R + K × (S − E) (S = 1, ½ or 0)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ra | Your rating | — |
rb | Opponent's rating | — |
k | K-factor | — |
rs | Result of the game | — |
E | Your expected score | % |
NA | Your new rating | — |
CH | Change in your rating | — |
NB | Opponent's new rating | — |
Worked example
- Your rating1500
- Opponent's rating1600
- K-factor20
- Result of the game1
- Your expected score36.0 %
- Your new rating1512.8
- Change in your rating12.8
- Opponent's new rating1587.2
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.