Elo Rating Calculator
Rating change after one game or a whole tournament, with FIDE K-factors
The Elo formula gives each player an expected score, E = 1 / (1 + 10^((Ropponent − Ryou) / 400)), and changes the rating by K × (actual score − E). A 1650 player who beats an 1800 player expects only 0.2966 of a point, so at K = 20 the win is worth +14.07 points with the formula and +14 under FIDE's official table: a new rating of 1664.
Last updated October 2026
Method: Classic Elo: E = 1 / (1 + 10^((Rb − Ra) / 400)) and a rating change of K × Σ(S − E). The FIDE option follows the FIDE Rating Regulations effective 1 March 2024: table 8.1.2, the 400-point rule of 8.3.1 (from 1 October 2025 only for players rated below 2650), the K-factors of 8.3.3 with the K × n ≤ 700 limit, and the rounding rule of 8.3.4.
Included: One game or any number of games, all three results side by side, the opponent's change, FIDE K presets or a custom K, a game-by-game breakdown and a win expectancy table.
Not included: The US Chess formula (explained, not computed), Glicko-type systems, initial ratings, rating floors and special rapid and blitz rules.
♟️ Rating calculation
♟️ Rating change (win)
⚖️ Every possible result
| Result | Your change | New rating | Opponent |
|---|---|---|---|
| Win | +14.07 | 1,664 | −14.07 |
| Draw | +4.07 | 1,654 | −4.07 |
| Loss | −5.93 | 1,644 | +5.93 |
The classic formula gives fractional points; most rating lists publish the result rounded to a whole number. The opponent column assumes the opponent uses the same K.
📊 Win expectancy by rating difference
| Gap | Favorite E | Underdog E | Favorite wins | Underdog wins |
|---|---|---|---|---|
| 0 | 50.0% | 50.0% | +10.0 | +10.0 |
| 50 | 57.1% | 42.9% | +8.6 | +11.4 |
| 100 | 64.0% | 36.0% | +7.2 | +12.8 |
| 150 | 70.3% | 29.7% | +5.9 | +14.1 |
| 200 | 76.0% | 24.0% | +4.8 | +15.2 |
| 250 | 80.8% | 19.2% | +3.8 | +16.2 |
| 300 | 84.9% | 15.1% | +3.0 | +17.0 |
| 350 | 88.2% | 11.8% | +2.4 | +17.6 |
| 400 | 90.9% | 9.1% | +1.8 | +18.2 |
| 450 | 93.0% | 7.0% | +1.4 | +18.6 |
| 500 | 94.7% | 5.3% | +1.1 | +18.9 |
| 550 | 96.0% | 4.0% | +0.8 | +19.2 |
| 600 | 96.9% | 3.1% | +0.6 | +19.4 |
| 650 | 97.7% | 2.3% | +0.5 | +19.5 |
| 700 | 98.3% | 1.7% | +0.3 | +19.7 |
| 750 | 98.7% | 1.3% | +0.3 | +19.7 |
| 800 | 99.0% | 1.0% | +0.2 | +19.8 |
Points for a win at K = 20. Expected score counts a draw as half a point, so it is not the same as the chance of winning outright.
Elo rating calculator: the formula, K-factors and FIDE rules explained
The Elo system, introduced by the physicist and chess master Arpad Elo, rates players by comparing results with expectations: beat someone you were expected to beat and you gain a little, beat someone you were expected to lose to and you gain a lot. Below are the formula, FIDE's current K-factor rules, how FIDE's lookup table differs from the formula, and how US Chess ratings work.
The Elo formula
For player A rated RA against player B rated RB:
EA = 1 ÷ (1 + 10^((RB − RA) ÷ 400)) R′A = RA + K × (SA − EA) E is the expected score between 0 and 1, S the actual score (1 win, 0.5 draw, 0 loss) and K the development coefficient that limits how far one result can move a rating. Both expected scores add up to 1, so with the same K one player's gain is the other's loss. Over several games, add up S − E before multiplying by K.
Worked example: a 1650 player beats an 1800 player
The gap is 150 points against the 1650 player: 10^(150 ÷ 400) = 10^0.375 = 2.3714, so E = 1 ÷ 3.3714 = 0.2966. With K = 20:
- Win: 20 × (1 − 0.2966) = +14.07, new rating 1664.07, published as 1664. The 1800 player loses 14.07.
- Draw: 20 × (0.5 − 0.2966) = +4.07.
- Loss: 20 × (0 − 0.2966) = −5.93, small because the loss was expected.
In FIDE's table a 150-point gap falls in the 146 to 153 band, where the lower-rated player's expected score is 0.30, so the changes are exactly +14, +4 and −6. K scales everything: the same win is worth +7.03 at K = 10 and +28.14 at K = 40.
What the expected score means
The 400 fixes the scale: a 400-point gap makes the favorite's expected score ten times the underdog's, 90.9% against 9.1%. Each 100 points multiplies the odds by 1.778, so a 100-point favorite expects 64.0%, a 200-point favorite 76.0% and an 800-point favorite 99.0%. A 75% expectation needs a gap of 190.8 points.
Expected score is not the chance of winning. It counts a draw as half a point, so it blends wins and draws: P(win) + 0.5 × P(draw). The formula predicts points, not how they are split.
Expected score for rating differences from 0 to 800
Formula versus FIDE table, with what each result is worth at K = 20 (computed with the calculator's own functions):
| Gap | Favorite E (formula) | FIDE table | Favorite win / draw / loss | Underdog win |
|---|---|---|---|---|
| 0 | 50.0% | 0.50 | +10.0 / 0.0 / −10.0 | +10.0 |
| 50 | 57.1% | 0.57 | +8.6 / −1.4 / −11.4 | +11.4 |
| 100 | 64.0% | 0.64 | +7.2 / −2.8 / −12.8 | +12.8 |
| 150 | 70.3% | 0.70 | +5.9 / −4.1 / −14.1 | +14.1 |
| 200 | 76.0% | 0.76 | +4.8 / −5.2 / −15.2 | +15.2 |
| 250 | 80.8% | 0.81 | +3.8 / −6.2 / −16.2 | +16.2 |
| 300 | 84.9% | 0.85 | +3.0 / −7.0 / −17.0 | +17.0 |
| 350 | 88.2% | 0.89 | +2.4 / −7.6 / −17.6 | +17.6 |
| 400 | 90.9% | 0.92 | +1.8 / −8.2 / −18.2 | +18.2 |
| 450 | 93.0% | 0.94 | +1.4 / −8.6 / −18.6 | +18.6 |
| 500 | 94.7% | 0.96 | +1.1 / −8.9 / −18.9 | +18.9 |
| 550 | 96.0% | 0.97 | +0.8 / −9.2 / −19.2 | +19.2 |
| 600 | 96.9% | 0.98 | +0.6 / −9.4 / −19.4 | +19.4 |
| 650 | 97.7% | 0.99 | +0.5 / −9.5 / −19.5 | +19.5 |
| 700 | 98.3% | 0.99 | +0.3 / −9.7 / −19.7 | +19.7 |
| 750 | 98.7% | 1.00 | +0.3 / −9.7 / −19.7 | +19.7 |
| 800 | 99.0% | 1.00 | +0.2 / −9.8 / −19.8 | +19.8 |
The FIDE column is the raw table value; players rated below 2650 have any gap over 400 counted as 400, capping them at 0.92. Up to 800 points the table and the formula never differ by more than 1.83 percentage points (at 560 points: 0.98 against 96.2%).
Choosing the K-factor
K is the most one game can move a rating. FIDE's regulations set it as follows:
- K = 40 for a player new to the rating list until they have completed events with at least 30 games, and for all players until the end of the year of their 18th birthday while rated under 2300.
- K = 20 as long as a rating remains under 2400.
- K = 10 once a published rating has reached 2400, even if it later drops.
- The 700 cap: if K times the games in a rating period exceeds 700, K becomes the largest whole number that keeps the product at or under 700. A junior at K = 40 playing 18 games gets K = 38, because 40 × 18 = 720.
FIDE's rapid and blitz regulations use the same K rules. Clubs and game systems outside FIDE often pick a fixed K such as 16, 24 or 32; use the custom option for those.
Worked example: a junior's five-game tournament
A 1500-rated junior (K = 40) beats 1620, draws 1480, loses to 1710, beats 1555 and beats 1390: 3.5 points against an average opponent of 1551. Every expected score uses the starting rating of 1500:
| Opponent | Result | Gap | E (formula) | S − E | E (FIDE) | S − E |
|---|---|---|---|---|---|---|
| 1620 | Win | −120 | 0.3339 | +0.6661 | 0.34 | +0.66 |
| 1480 | Draw | +20 | 0.5288 | −0.0288 | 0.53 | −0.03 |
| 1710 | Loss | −210 | 0.2299 | −0.2299 | 0.23 | −0.23 |
| 1555 | Win | −55 | 0.4215 | +0.5785 | 0.42 | +0.58 |
| 1390 | Win | +110 | 0.6532 | +0.3468 | 0.65 | +0.35 |
| Total | 3.5 | 2.1672 | +1.3328 | 2.17 | +1.33 |
With the formula the change is 40 × 1.3328 = +53.31; under FIDE rules 40 × 1.33 = 53.2, rounded to +53. Either way the new rating is 1553, and K × n = 200 stays well under the 700 cap. The "Worked example" button in tournament mode loads these games.
How FIDE's calculation differs from the formula
FIDE reads the expected score, which it calls PD, from table 8.1.2 of its Rating Regulations: rating-difference bands from 0 to 3 points (0.50) up to 620 to 735 points (0.99), and 1.00 beyond. Three more rules matter:
- The 400-point rule. Below 2650, a gap over 400 counts as 400; since October 1, 2025 players rated 2650 and above use the real gap. When a 2700 player beats a 2200 player, the 2700 player's expected score is 0.96, so at K = 10 the win is worth 0.4, rounded to 0 (under the old rule, 0.92 and +1). The 2200 player is still capped: expected score 0.08, and at K = 20 the loss costs 1.6, rounded to 2.
- Rounding. The change for a rating period is rounded to the nearest whole number, 0.5 away from zero, on the total rather than per game.
- Floor. A first rating must be at least 1400, and players who drop below 1400 are shown as unrated on the next list.
In rapid and blitz, FIDE applies the 400-point rule to everyone and, from December 1, 2024, does not rate games between players whose ratings differ by 600 points or more when at least one of them is rated above 2600.
USCF rating calculator: how US Chess ratings differ
US Chess ratings follow the US Chess Rating System by Mark Glickman and Thomas Doan (April 6, 2026 version). For players with more than 8 games it uses the same logistic expectancy, but K depends on experience and rating: K = 800 ÷ (N′ + m), with m the games in the event and N′ an "effective number of games" of at most 50, smaller for lower-rated players. In the document's own example a 1700 player with 30 games has N′ = 20, so in a four-game event K = 800 ÷ 24 = 33.33, against FIDE's 20.
- Bonus points reward results far above expectation in events of three or more games; the multiplier B has been 10 since January 1, 2025.
- A special formula applies to players with 8 or fewer games, or with all wins or all losses.
- Rating floors start at an absolute 100; established players get a floor 200 points below their peak, in 100-point steps from 1200 to 2100.
- Six ratings exist: regular, quick and blitz, each over the board and online.
This calculator therefore does not reproduce US Chess results; check the rating report US Chess publishes after your event for official numbers.
How to use it, and who it is for
- Choose One game or Tournament; tournament mode takes any number of games.
- Enter your rating and, for one game, the opponent's rating and the result.
- Pick your K-factor, or a custom value for your club or game.
- Choose the method: the formula gives exact decimals; the FIDE table reproduces an official calculation with the 400-point rule, the 700 cap and rounding.
Club players use it to preview what a result is worth, arbiters and organizers to verify crosstables, coaches to set realistic targets with the expectancy table, and developers to rate players in their own games and leagues.
Key terms
- Expected score (E or PD): predicted points per game, counting a draw as half.
- K-factor: the multiplier that sets how much one result moves a rating.
- Rating period: the games rated together on one list, all against the starting rating.
- Effective number of games (N′): the US Chess measure of how settled a rating is.
What changes the result
The rating gap sets the expected score and K sets the size of the change. The method matters less: table and formula agree within a point for most games, but rounding can turn +0.4 into 0 or −1.6 into −2. Updating the rating after every game instead of once per event changes the total slightly, which is why FIDE scores all games against the starting rating. Above a 400-point gap, the player's own rating decides whether the cap applies.
Tips and limitations
- Check your K before comparing with an official report; at K = 40 a rating moves twice as fast as at K = 20.
- Enter all games of a rating period together instead of chaining single-game results.
- A draw with a much weaker player costs points: 7 at a 300-point gap and K = 20.
- Unrated players, initial ratings, floors, the US Chess bonus and Glicko-type online ratings are outside this tool.
Related calculators
- To track your score percentage over many games, use the Win Rate Calculator; for chances of combined outcomes, the Probability Calculator.
- To see how 10^(D ÷ 400) behaves, try the Logarithm Calculator; for another sports rating, the Golf Handicap Calculator.
Sources
- FIDE Handbook, FIDE Rating Regulations effective from 1 March 2024 (table 8.1.2, rules 8.3.1 to 8.3.4, rating floor).
- FIDE Handbook, FIDE Rapid and Blitz Rating Regulations.
- US Chess Federation, The US Chess Rating System, Glickman and Doan, April 6, 2026.
- Elo, A. E., The Rating of Chessplayers, Past and Present (1978), the original description of the system.
⚠️ Common mistakes & edge cases
Updating the rating after every game
FIDE scores every game of a rating period against the starting rating; chaining updated ratings gives a slightly different total.
Using the wrong K-factor
A 17-year-old rated 1900 uses K = 40, not 20, and a player who once reached 2400 stays at K = 10. The wrong K doubles or halves every change.
Forgetting the 400-point rule
Below 2650 a 500-point gap counts as 400 (0.92 instead of 0.96); above 2650 the real gap applies, so one game can be scored differently for each player.
Reading expected score as the chance of winning
76% at a 200-point gap is a points forecast that includes draws; the actual winning percentage is usually lower.
Mixing rating pools
FIDE, US Chess and online ratings use different scales and formulas. Combining them gives a number that matches none.
Rounding every game separately
Five changes of +0.4 round to 0 each but add up to +2. FIDE rounds only the period total.
❓ Frequently asked questions
How do I calculate my new Elo rating after a game?
Find your expected score, E = 1 / (1 + 10^((opponent's rating − your rating) / 400)), subtract it from your result (1 win, 0.5 draw, 0 loss), multiply by your K-factor and add that to your rating. A 1650 player who beats an 1800 player has E = 0.2966, so at K = 20 the new rating is 1650 + 20 × (1 − 0.2966) = 1664.07, published as 1664.
What does the 400 in the Elo formula mean?
It sets the scale: a 400-point gap means the stronger player's expected score is ten times the weaker player's, 90.9% against 9.1%. A 200-point gap gives 76.0%, 100 points 64.0% and 800 points 99.0%.
What K-factor should I use?
Under FIDE rules, K is 40 for a new player until they have completed events with at least 30 games, and for all players until the end of the year of their 18th birthday while rated under 2300. K is 20 while a rating stays under 2400 and 10 once a published rating has reached 2400. If K times the games in a rating period exceeds 700, K drops to the largest whole number that keeps the product at or under 700.
How many points do I gain for beating a higher-rated player?
At K = 20, beating someone rated 100 points higher earns 12.8 points, 200 points higher about 15.2 and 300 points higher about 17.0 with the Elo formula. FIDE's table rounds these to 13, 15 and 17. One game can never earn more than K.
How many Elo points is a draw worth?
K × (0.5 − E). Against an equal opponent nothing changes; against someone 100 points higher a draw earns about 2.8 points at K = 20, and against someone 300 points higher about 7.0. The higher-rated player loses the same amount.
How does a USCF rating calculator differ from an Elo calculator?
US Chess uses the same logistic expected score for players with more than 8 games, but its K-factor is K = 800 / (N' + m), where N' is an effective number of games (at most 50) and m the games in the event. It adds bonus points for unusually strong results (multiplier B = 10 since January 1, 2025), uses a special formula for players with 8 or fewer games and applies rating floors. This calculator computes the standard Elo and FIDE methods, not the US Chess formula.
What is the FIDE 400-point rule?
A rating difference of more than 400 points counts as 400, which limits the expected score to 0.92 and 0.08. Since October 1, 2025 it applies only to players rated below 2650; players rated 2650 and above use the actual difference, so a 2700 player facing a 2200 player has an expected score of 0.96.
How do I calculate the rating change for a whole tournament?
Compute the expected score for each game from your rating at the start of the event, add up actual minus expected across all games and multiply by K. A 1500 player at K = 40 who scores 3.5 from five games with an expected total of 2.17 under the FIDE table gains 40 × 1.33 = 53.2, rounded to 53.
What rating difference gives a 75% expected score?
About 191 points with the Elo formula (190.8, from 400 × log10(0.75 / 0.25)). In FIDE's table, gaps of 189 to 197 points give 0.75. A 90% expectancy needs about 382 points.
Is expected score the same as win probability?
No. Expected score counts a draw as half a point: expected score = P(win) + 0.5 × P(draw). A 64% expectation could mean winning 50% of games and drawing 28%, or winning 64% and never drawing.
💡 Good to know
Ten to one at 400 points
Every 400 points multiplies the favorite's expected score relative to the underdog's by ten. At 800 points the ratio is 100 to 1, an expected score of 99.0%.
The most you can win is K
A win can never be worth more than K points. At K = 20, beating someone 800 points stronger earns 19.8 points with the formula.
Not only for chess
The formula works for any two-player contest with wins, draws and losses; choose a starting rating and a K that suits how often players compete.