How Chess Ratings Work: Elo, FIDE Ratings and Puzzle Ratings

Every competitive chess player has a rating: a single number that measures playing strength. It goes up when you win, down when you lose, and it lets players who have never met predict who will win. Here is how it works, and what the numbers mean.

The Elo system

Most chess ratings come from the Elo system, invented by the Hungarian-American physics professor Arpad Elo. The US Chess Federation adopted it in 1960, and FIDE in 1970.

The idea is simple: your rating predicts your score, and after each game the rating moves by how much better or worse you did than predicted.

Step 1: the expected score

Given two ratings, the expected score of player A against player B is:

Expected = 1 / (1 + 10^((Rating B - Rating A) / 400))

The only thing that matters is the difference in rating:

Step 2: the update

After the game:

New rating = Old rating + K × (Score - Expected)

where the score is 1 for a win, ½ for a draw and 0 for a loss, and K (the K-factor) sets how fast ratings move.

A worked example

A player rated 1500 plays one rated 1700, with K = 20. The 1500 player's expected score is about 0.24.

• Win: 20 × (1 - 0.24) = +15
• Draw: 20 × (0.5 - 0.24) = +5
• Loss: 20 × (0 - 0.24) = -5

Beating a stronger player earns a lot; losing to them costs little. Against a weaker player it is the other way round. That is what makes the system fair: you can only climb by scoring better than your rating predicts.

FIDE ratings

FIDE, the international chess federation, publishes official ratings every month for classical, rapid and blitz chess. Its K-factors:

• K = 40 for new players, until they have played 30 rated games, and for juniors under 18 rated below 2300.
• K = 20 for players rated below 2400.
• K = 10 for players who have reached 2400.

The lowest FIDE rating is 1400, after a change in 2024 that also raised the ratings of lower-rated players.

What is a good rating?

The highest rating ever recorded is Magnus Carlsen's 2882, in 2014.

Titles

Ratings are also part of the titles players can earn:

A norm is an exceptional result in a strong tournament against titled players. The GM title is for life.

Online ratings

Chess sites use their own pools of players, so their numbers are not the same as FIDE ratings. Lichess and Chess.com use Glicko systems, a refinement of Elo by Mark Glickman that also tracks how certain the rating is: a new player's rating moves quickly, then settles as the system learns more about them. Online ratings in fast time controls also tend to be spread more widely than over-the-board ratings.

So do not compare a 1500 online rating with a 1500 FIDE rating - they measure different things.

Puzzle ratings

Puzzle ratings use the same maths. Each puzzle has a rating too, and solving it counts as a game against it: solve a hard puzzle and you gain a lot; miss an easy one and you lose a lot.

On ChessKite, everyone starts at 1000, and the rating uses the standard Elo formula. There is one twist: the feed deliberately serves puzzles you will solve most of the time, to keep you in a flow - so rating every card would measure the feed's choices more than your skill. Instead, roughly one card in eight is a challenge card at your true level, and only those are rated (with a larger K, 32, so each one counts).

A puzzle rating measures tactical vision, not your whole game - but the two are closely linked. A rising puzzle rating almost always shows up in your games.

Climb your rating

The fastest way to gain rating at almost every level is to make fewer tactical mistakes and spot more of your opponent's. Start the puzzle feed, keep a streak with the Daily puzzles, and test your speed in Compete. Then read how to get better at chess for a full training plan.