Elo Rating Calculator
Work out the expected score and the rating change after one game, by the Elo formula or by the FIDE rating regulations with their table and 400-point rule.
Result
New rating: 1,515
One game against one rated opponent. A federation rates a whole tournament or rating period at once, with its own K and rules.
- Rating change
- 15.2
- Expected score
- 0.24
https://calcgallery.com/sports/elo-rating-calculator/
Results are exact arithmetic on the numbers you enter, following the rule or formula the page names. Official records are kept by the league, federation or association concerned, and their figures and rulings control. Read the full disclaimer
How to use the Elo Rating Calculator
- Enter your rating, your opponent's rating and the result of the game.
- Enter the K factor your federation or league gives you. FIDE's values are one tap away.
- Choose how the expected score is found, the Elo formula or FIDE's table, and read your new rating and the change.
The Elo formula
The Elo system assumes each rating estimates a playing strength, and that the expected score depends only on the difference between two ratings:
E = 1 ÷ (1 + 10^(−(your rating − opponent's rating) ÷ 400))R′ = R + K × (S − E)A 400-point gap gives the stronger player an expected score of about 0.91. Each game nudges the rating towards the strength the result suggests, by an amount set by K.
The FIDE regulations
FIDE’s rating regulations use a table instead of the formula. Regulation 8.1.2 lists the rating difference in bands and gives the higher-rated player’s score probability for each, from 0.50 for a difference of 0 to 3 points up to 0.99 for 620 to 735. Since 1 October 2025, regulation 8.3.1 counts a difference of more than 400 points as 400 for a player rated below 2650, so a strong player gains a little more from beating a much weaker one. The change for the rating period is rounded to a whole number, a half away from zero.
One game at a time
The page rates a single game against a rated opponent. Federations rate a tournament or a month at once, with rules for unrated opponents, provisional ratings and caps on K that a one-game page does not model.
With your numbers
- E = 1 ÷ (1 + 10^(−(1,500 − 1,700) ÷ 400)) = 0.24
- Change = 20 × (1 − 0.24) = 15.2
- New rating = 1,500 + change = 1,515
Quick reference
One game against one rated opponent. A federation rates a whole tournament or rating period at once, with its own K and rules.
| Example | New rating |
|---|---|
| 1500 beats 1700, K 20 | 1,515 |
| 1500 draws with 1700, K 20 | 1,505 |
| 1500 loses to 1700, K 20 | 1,495 |
| Equal players, 1600 wins, K 32 | 1,616 |
| FIDE: 1500 beats 1700, K 20 | 1,515 |
| FIDE: 2000 beats 1500, the 400-point rule | 2,002 |
| FIDE: 2700 beats 2200, K 10, no cap | 2,700 |
| FIDE: 1800 loses to 1000, K 40 | 1,763 |
Common questions about the Elo Rating Calculator
- What is an expected score?
- The score the ratings predict for you in one game, counting a win as 1, a draw as a half and a loss as 0. Rated 200 points below your opponent, the Elo formula expects about 0.24, a quarter of a point. Win, and you beat that expectation by 0.76 points.
- How much does one game change a rating?
- K times the difference between your score and your expected score. With K = 20, beating a player 200 points above you adds 20 × 0.76, about 15 points. Losing to them costs 20 × 0.24, about 5, because the loss was mostly expected.
- Why do the two methods give slightly different answers?
- FIDE does not use the formula. Its regulations convert the rating difference to a score probability with table 8.1.2, count any difference beyond 400 points as 400 for players under 2650, and round the change to a whole number. The formula has no cap and no rounding. The two agree to within about a point for most games.
- Which K factor should I use?
- The one your rating body assigns you. FIDE uses 40 for new players and juniors under 2300, 20 below 2400 and 10 once a player has reached 2400. Other federations and online sites set their own.
- Can I rate a whole tournament?
- Run the page once per game with your pre-tournament rating each time, then add the changes. Both FIDE and the Elo system add the per-game changes for the rating period rather than updating after every game. FIDE then rounds the total once, so the sum of rounded single games can differ from it by a point.