How the Elo rating system works
The Elo system, named after its creator Arpad Elo (1903-1992), is the reference method for measuring the strength of chess players. Adopted by FIDE (the International Chess Federation) in 1970, it relies on a simple principle: every player has a numerical rating that changes according to their results against other rated players.
The Elo system is based on the concept of relative strength. The core idea is that the probability of winning a game depends on the rating difference between the two players. The bigger the gap, the more likely the higher-rated player is to win. This probability follows a logistic distribution.
The winning probability formula
The expected score of player A against player B is calculated as follows:
We = 1 / (1 + 10(RB - RA) / 400)
The factor 400 is a calibration constant chosen so that a 200-point difference gives the higher-rated player about a 75% chance. A 400-point difference gives about a 91% probability of winning.
FIDE applies a 400-point cap on the rating difference: if the actual difference exceeds 400 points, the calculation uses 400. This rule prevents excessive swings in very lopsided games.
The K-factor explained
The K-factor determines how much the rating moves after each game. A high K means the rating reacts strongly to results; a low K makes it more stable.
FIDE uses three K values:
- K = 40: for players with fewer than 30 rated games, or for players under 18 whose rating has never reached 2300.
- K = 20: for players rated below 2400.
- K = 10: for players who have reached 2400 at least once. K stays at 10 even if the rating drops afterwards.
This scale lets young players progress quickly when their real strength exceeds their rating, while keeping ratings stable for experienced players whose level is well established.
What is my Elo rating worth?
The Elo rating lets you see where you stand compared with other players. Here are the commonly accepted ranges:
| Elo rating | Level |
|---|---|
| 1000 - 1200 | Beginner |
| 1200 - 1400 | Casual / occasional player |
| 1400 - 1600 | Intermediate club player |
| 1600 - 1800 | Good club player |
| 1800 - 2000 | Strong club player |
| 2000 - 2200 | Expert / Candidate Master |
| 2200 - 2300 | Candidate Master (CM) |
| 2300 - 2400 | FIDE Master (FM) |
| 2400 - 2500 | International Master (IM) |
| 2500+ | Grandmaster (GM) |
| 2700+ | Super Grandmaster (world elite) |
| 2800+ | World top 10 |
Worked example
Let's take a player rated 1800 facing an opponent rated 2005. The gap is 205 points against our player.
Step 1: Expected score
D = 1800 - 2005 = -205
We = 1 / (1 + 10205/400) = 1 / (1 + 3.26) ≈ 0.235
The 1800 player has about a 23.5% chance of scoring the point.
Step 2: New rating
With K = 20, depending on the result:
- Win (W = 1): Δ = 20 × (1 - 0.235) = +15.3 → New Elo ≈ 1815
- Draw (W = 0.5): Δ = 20 × (0.5 - 0.235) = +5.3 → New Elo ≈ 1805
- Loss (W = 0): Δ = 20 × (0 - 0.235) = -4.7 → New Elo ≈ 1795
Notice that a draw against a stronger player gains points, because the actual score (0.5) is higher than the expected score (0.235).
Frequently asked questions
Is Elo an acronym?
No, Elo is not an acronym. It is the surname of Arpad Elo (1903-1992), the Hungarian-born American physicist who created this rating system in the 1960s.
What is the difference between FIDE Elo and national Elo?
The FIDE rating is the official international rating, calculated only from FIDE-rated tournaments. National ratings (such as the FFE rating in France) also include local tournaments. Both use the same formula but with different games, which can create gaps of 50 to 150 points.
How do I get my first FIDE rating?
To get an initial FIDE rating, you must play at least 5 games against FIDE-rated players in rated tournaments and reach a score high enough to calculate a valid performance.
Why is my online rating (Lichess/Chess.com) different from my FIDE rating?
Online platforms use the Glicko or Glicko-2 system, not pure Elo. Glicko includes a measure of uncertainty (RD - Rating Deviation) and adjusts ratings faster when uncertainty is high. Moreover, the level of online players can differ from over-the-board classical play: thinking time, psychological pressure and the absence of potential cheating all change the picture.
What is an Elo performance rating?
The Elo performance represents the theoretical level at which you played in a tournament. It is calculated from your opponents' average rating and your percentage score, using the FIDE conversion table. A performance of 2400 in a tournament means you played like a 2400-rated player during that event.
Sources and references
This calculator implements the rules defined in the FIDE Rating Regulations (official FIDE rules). The formulas and the D(p) table comply with the current specifications.
To learn more, read the Elo rating system on Wikipedia article.