Elo Rating Calculator
See your new chess or game rating after a win, draw or loss, and your expected score against any opponent. Advanced adds several games at once, performance rating and the result you need.
Organisations set their own K-factors; check your federation’s rules. A bigger K means bigger swings.
Rating gap → expected score table (0–800 points)
| Gap | Higher-rated expects | Lower-rated expects | Higher-rated: win / draw / loss (K 20) |
|---|
Your gap is highlighted. A win/draw/loss swing for the lower-rated player is the same size with the sign flipped (same K).
How your new rating is worked out
Your numbers, step by step. Change = K × (score − expected score).
- 1
Rating gap
1600 − 1500 = 100
- 2
Expected score
1÷(1+10^(100÷400))
= 0.360 - 3
Score minus expected
1 − 0.360 = +0.640
- 4
Times your K-factor
20 × 0.640 = +12.8
1500 → 1512.8
Read more: the formula, a worked example, an expected-score table and notes
The Elo system, named after the physicist and chess player Arpad Elo, compares how you actually scored with how you were expected to score. Beat someone rated higher and you gain more; lose to someone rated lower and you drop more. The same maths is used for many other games and sports.
The formula
expected score = 1 ÷ (1 + 10 ^ ((opponent rating − your rating) ÷ 400))
score = 1 for a win, ½ for a draw, 0 for a loss
rating change = K-factor × (score − expected score)
new rating = old rating + rating change
Several games: change = K × (total score − total expected score)
Performance (linear) = average opponent + 400 × (wins − losses) ÷ games
The expected-score performance is the rating that would expect exactly your score against the same opponents. It can’t be worked out for a perfect score or a zero.
Worked example
You are rated 1500 and beat a 1600 player, with K = 20. The gap is 1600 − 1500 = 100, and 100 ÷ 400 = 0.25. 10^0.25 = 1.7783, so your expected score is 1 ÷ (1 + 1.7783) = 1 ÷ 2.7783 = 0.3599 (about a 36% share). You scored 1, so the change is 20 × (1 − 0.3599) = 20 × 0.6401 = +12.8, and your new rating is 1512.8 (1513 if rounded). Your opponent expected 0.6401 and scored 0, so they lose 20 × 0.6401 = 12.8 and drop to 1587.2. A draw would have given you 20 × (0.5 − 0.3599) = +2.8, and a loss 20 × (0 − 0.3599) = −7.2.
Expected score by rating gap
| Gap | Higher-rated | Lower-rated |
|---|---|---|
| 0 | 0.50 | 0.50 |
| 50 | 0.57 | 0.43 |
| 100 | 0.64 | 0.36 |
| 200 | 0.76 | 0.24 |
| 300 | 0.85 | 0.15 |
| 400 | 0.91 | 0.09 |
| 600 | 0.97 | 0.03 |
| 800 | 0.99 | 0.01 |
Notes
- K-factor. Organisations set their own K-factors, and often use different values for new, young, strong or very active players. Check your federation’s or club’s rules for the K that applies to you.
- Win chance. Elo gives an expected share of the points, not separate chances of a win, draw and loss. 0.36 could be 36 wins and 64 losses from 100 games, or fewer wins with some draws.
- Several games. Many events work out every game from your rating at the start and add the changes up at the end. That’s what this calculator does. Some online sites update after every game instead, which gives slightly different totals.
- Rounding and limits. Some bodies round each change, cap the rating gap they count, or have rating floors. Results here aren’t rounded until the end.
- Teams. For team or doubles games, a common shortcut is to average each side’s ratings and treat the averages as two players.
- Other systems. Some online platforms use Glicko or Glicko-2, which also track how sure they are of your rating, so their changes won’t match plain Elo.
Common questions
How is an Elo rating change worked out?
First find your expected score: 1 ÷ (1 + 10^((opponent − you) ÷ 400)). A win scores 1, a draw ½ and a loss 0. Your change is K × (score − expected score). Beating a 1600 player when you are 1500, with K = 20, gives 20 × (1 − 0.36) = about +12.8.
What K-factor should I use?
Organisations set their own K-factors, and many use a bigger K for new or young players and a smaller one for strong or very active players. Check your federation’s or club’s own rules. A bigger K makes ratings move faster in both directions.
What does a 200-point rating gap mean?
The higher-rated player is expected to score about 0.76 points a game, or 76 points from 100 games. Elo can’t split this into wins and draws: 0.76 could be 76 wins and 24 losses, or a mix with draws.
What is a performance rating?
The rating you played at in an event. The quick linear method is average opponent rating + 400 × (wins − losses) ÷ games. The expected-score method finds the rating whose expected score against the same opponents equals the score you made.
Is the rating change the same for both players?
When both players use the same K-factor, yes: what one gains, the other loses. If their K-factors differ, the changes differ too.
Related calculators
Made by Zulu Calculator, part of AlphaZulu LLC. Formulas are shown in full and rule figures are checked against official sources; see how we build calculators.