Elo Calculator

What a result is actually worth

A rating is a prediction, not a trophy. Elo turns the gap between two ratings into an expected score - the share of the point the stronger player should take if the ratings are right - and then moves both ratings by however much the actual result disagreed with that prediction. Beat someone you were supposed to beat and almost nothing happens. Beat someone you were not supposed to beat and the system moves you a long way, because it has just learned that it was wrong about you.

That is the whole system, and it fits in one line: your new rating is your old rating plus K times the difference between what you scored and what was expected. Everything else - the K-factor, the 400-point cap, the way a draw against a stronger player is a gain - is detail on top of that line. This page writes the line out with your numbers in it rather than handing you an answer and asking you to trust it.

It also shows all three results at once. "What do I get for winning" and "what do I lose if I don't" are the same question asked twice, and knowing both before the game is more useful than knowing one after it.

How the Elo system works

• The expected score comes only from the gap. A 200-point favourite is expected to score 76% of the points available, whether the ratings are 1200 and 1000 or 2600 and 2400. That is what makes the scale meaningful across its whole range.
• The K-factor is how much one event is allowed to move a rating. FIDE uses 40 while a player has fewer than 30 rated games and for under-18s still rated below 2300, 20 for an established player under 2400, and 10 once a rating has EVER reached 2400 - the trigger is the historical peak, so a master who drops back keeps the slow factor.
• A rating difference of more than 400 points counts as exactly 400. Without that cap, a 2600 beating a 900 would be predicted to score 0.9999 and would lose almost a whole point of rating for the privilege - the model stops being useful long before the gap gets that wide, so FIDE simply stops widening it.
• A draw is not a neutral result. Against someone 200 points higher your expected score is 0.24, so half a point beats the prediction and your rating goes up. Against someone 200 points lower the same half point costs you.
• Ratings are zero-sum within a game: whatever you gain, your opponent loses, as long as you are both on the same K-factor. When the K-factors differ - a junior against a veteran - the pair genuinely does not balance, which is where rating inflation and deflation arguments start.

How to work out your new rating

1. 1

   Enter your rating and how many rated games you have played

   The games count is only there to pick the K-factor: under 30 games FIDE uses 40, which is why a new player's rating swings so hard. If you already know your K-factor, type it in the third box and it overrides everything.

2. 2

   Add each opponent and the result

   One row per game. For a single game the page also shows what the other two results would have done, which is the number worth knowing before you sit down rather than after.

3. 3

   Read the answer, then the working

   The new rating and the change are at the top; the expected score, your actual score and the K-factor sit beside them. Underneath, each step of the formula is written out with your numbers substituted in.

4. 4

   Check the performance rating for a whole event

   After several games the page also reports what you performed at - the average opponent plus 400 times wins minus losses over games played. It is the standard approximation, and it is what tournament reports mean by "a 2100 performance".

What a rating gap is worth

The share of the points each side is expected to take, from the rating difference alone. The curve is symmetric, so the two columns always add to 100%.

Worked examples

Common mistakes

• Assuming your online rating is Elo. Chess.com and Lichess both run Glicko variants, which track how uncertain a rating is as well as its value. That is why a new online account can move 100 points in an evening and no Elo K-factor would allow it.
• Comparing ratings across systems. A 1600 on Chess.com, a 1600 on Lichess and a 1600 FIDE are three different strengths. The number is only meaningful inside the pool it was earned in.
• Forgetting the 400-point cap. It only bites in lopsided games, but when it does it changes the answer substantially - and it is the reason a calculator that skips it disagrees with the arbiter's sheet.
• Rating each game of a tournament separately. FIDE sums the expected scores over the whole event and applies K once at the end. Applying it game by game with an updated rating each time gives a different, wrong number.
• Using K = 40 forever. It is the beginner's factor and it is meant to expire: after 30 rated games your rating is supposed to have found its level, and a K that stays high keeps it permanently noisy.
• Reading a performance rating as a rating. Over four games it has enormous error bars - and the linear formula breaks completely at 100% or 0%, where it just returns the average opponent plus or minus 400.

Elo calculator FAQ