What Is an Elo Rating and How Is It Calculated?
An Elo rating is a numerical skill score for competitors in head-to-head games, where the difference between two ratings predicts the expected result and each game result moves both ratings by an equal and opposite amount. It was created by physicist Arpad Elo and adopted by the World Chess Federation (FIDE) in 1970.
The Elo formula has two steps. First, the expected score: EA = 1 ÷ (1 + 10(RB − RA) ÷ 400), where RA is your rating and RB is your opponent's. Second, the update: R′A = RA + K × (S − EA), where K is the K-factor and S is the actual score (1 for a win, 0.5 for a draw, 0 for a loss).
A 200-point rating advantage gives the stronger player an expected score of about 76%, and a 400-point advantage gives about 91%. Because the scale is built on a 400-point divisor, every 400 points of difference multiplies the odds of winning by ten.
How to Use This Elo Rating Calculator
Enter both ratings, pick a K-factor and choose the game result. The calculator updates instantly. Here's what each field means:
- Your rating / Opponent rating: Current Elo ratings of both players or teams. Club players typically sit between 1000 and 2000; FIDE-titled masters are above 2200.
- K-factor: The maximum swing from one game. FIDE uses K = 40 for new players, K = 20 for most players and K = 10 for players who have reached 2400.
- Game result: Win, draw or loss from your point of view. The cards below the main result show the rating change for all three outcomes.
The Elo system is used well beyond chess — in Go, esports, table tennis, football rankings and online matchmaking — and each organisation sets its own K-factor, so check your platform's rules for the exact value.
What Does an Elo Rating Difference Mean?
The table below shows the expected score for the higher-rated player at common rating gaps, using the standard 400-point logistic Elo curve.
| Rating Gap | Higher-Rated Expected Score | Lower-Rated Expected Score |
|---|---|---|
| 0 | 50.0% | 50.0% |
| 100 | 64.0% | 36.0% |
| 200 | 76.0% | 24.0% |
| 300 | 84.9% | 15.1% |
| 400 | 91.0% | 9.0% |
Frequently Asked Questions
How do you calculate Elo rating change?
Calculate the expected score as 1 ÷ (1 + 10^((opponent − your rating) ÷ 400)), then multiply K by the difference between your actual score (1, 0.5 or 0) and that expected score. Add the result to your rating.
What is a good K-factor?
FIDE uses K = 40 for new players and those under 18 rated below 2300, K = 20 for most other players, and K = 10 once a player has reached 2400. Online platforms often use values between 16 and 32 depending on the game.
What is the difference between Elo and Glicko?
Elo tracks a single rating number, while Glicko, created by Mark Glickman in 1995, adds a rating deviation that measures uncertainty and grows when a player is inactive. Glicko therefore adjusts faster for new or returning players, whereas Elo relies on a fixed K-factor.
How accurate is this Elo calculator?
It applies the standard Elo formulas exactly and rounds only for display. Real federations may round changes to whole points, apply rating floors, or use different K-factors, so official results can differ by a point or so.