Elo Rating Calculator
Your expected score and Elo rating change after one game or a whole event, for a win, draw or loss at the K-factor you choose.
Result…
How it's calculated
Expected score E = 1 ÷ (1 + 10^((Rb − Ra) ÷ 400)) Rating change Δ = K × (S − E), with S = 1 for a win, 0.5 for a draw, 0 for a loss Over several games: Δ = K × (Σ S − Σ E)
The Elo system predicts a score from the rating gap: a player 400 points stronger is expected to score about 0.91 per game, and equal players 0.5. After the game the rating moves by K times the difference between what happened and what was expected, so beating a stronger player gains more than beating a weaker one. The K-factor sets how fast ratings move; FIDE's values are in its rating regulations, and other bodies choose their own.
Your numbers, step by step
About the Elo Rating calculator
This Elo calculator shows how much a rating should move after a game or a whole event. Enter your rating, then each opponent's rating with the result, one game per line, such as 1600 W, 1500 D or 1700 L. It works out the expected score from the rating gap with E = 1 ÷ (1 + 10^((Rb − Ra) ÷ 400)) and the change Δ = K × (S − E) at the K-factor you choose, whether that is a chess federation's value, a club's or a game website's. For a single game it also lists the change for a win, a draw and a loss, so you can see what is at stake before you play. There is an option to count rating gaps of more than 400 points as 400, as FIDE does for most players. Every game's working is shown.
How to use it
- Enter “Your rating” before the games.
- Under “Games: opponent rating and result, one per line”, type each opponent's rating followed by W, D or L.
- Set the “K-factor” your federation, club or site uses.
- Choose whether to “Count gaps over 400 points as 400”.
- Read the new rating, the change, and the expected and actual scores.
Worked example
A 1500 player beats a 1700 player with K = 20. The expected score is 1 ÷ (1 + 10^(200 ÷ 400)) = 0.24, so the rating rises by 20 × (1 − 0.24) = 15.2 points to 1515.2. A draw would have gained 5.2 points and a loss cost 4.8. Over four games against 1600, 1500, 1700 and 1450 scoring 2.5, the expected total is 1.67, so the change is 20 × (2.5 − 1.67) = 16.6 points.
Updated
Questions people ask
How do I calculate an Elo rating change?
Find the expected score E = 1 ÷ (1 + 10^((opponent − you) ÷ 400)), subtract it from your actual score (1, 0.5 or 0), and multiply by K. Add the result to your rating.
What K-factor should I use?
Use the one your rating body sets. FIDE's rating regulations use K = 40 for players new to the list until they have 30 games, 20 while a rating stays under 2400, and 10 once it has reached 2400. Online sites and other games choose their own.
What does the expected score mean?
It is the average score the rating gap predicts per game, counting a draw as half. Against an equal opponent it is 0.5; 400 points stronger gives about 0.91.
Why did I lose points even though I drew?
If your opponent was rated lower, you were expected to score more than 0.5, so a draw is below expectation and costs a little. A common mistake is thinking a draw always leaves the rating unchanged.
Should I update my rating after each game or at the end?
Rating lists usually score every game in a rating period against your rating at the start, which is what this calculator does. Updating after each game gives a slightly different total.
Will this match my official rating change exactly?
It can differ by a point or so. FIDE reads expected scores from its own table and rounds, and other bodies add their own rules, so check the published figure. For general odds questions, the probability calculator may help.