Elo Calculator
See how a single game moves your Elo. Enter your rating, your opponent's rating, the result (win, draw, or loss), and a K-factor to get your win probability and new rating.
Example: with Your rating 1500 · Opponent's rating 1600 · Result Win · K-factor 32 — general / club use → New rating: 1,520.
- Rating change+20 points
- Expected score36.0% expected score
Computed by the calculator below using its default values. Change any input to see your own numbers.
Expected score E = 1 / (1 + 10^((opponent − you)/400)); new rating = old + K × (result − E). Beating a higher-rated player earns more than beating a weaker one.
How Elo turns a result into points
Elo does not care only whether you won — it cares whether you were supposed to. Before the game it computes an expected score from the rating gap: a number between 0 and 1 that is your average points if you played this opponent many times. A 400-point edge implies roughly a 10-to-1 expectation, about 0.91.
After the game it compares what happened to that expectation and moves your rating by K times the difference. Do better than expected and you gain; do worse and you lose. Because both players share the same expected-score math, the points one gains the other loses.
Why the K-factor changes everything
K sets how far a single result can move you. A large K (say 40) lets new players find their level quickly but makes ratings jumpy. A small K (10) keeps established masters stable, so one upset barely dents them. That is why federations lower K as you play more games or climb in rating.
The 400 constant is a scaling choice baked into the system by Arpad Elo. It defines what a rating point means: how much of a skill gap maps to how much expected-score advantage.
How it’s calculated
For one game, expected score E = 1 / (1 + 10^((Ropp − Ryou)/400)). New rating = Ryou + K × (S − E), where S = 1 for a win, 0.5 for a draw, and 0 for a loss. The 400 constant means a 400-point gap corresponds to about a 10:1 expected-score ratio.
One game at a time. Provisional-rating rules, rating floors, and multi-game period updates differ by system (FIDE, USCF, and Glicko-based online sites).
Common K-factors
| K-factor | Applies to | System |
|---|---|---|
| 40 | New players (first 30 games) or juniors | FIDE provisional |
| 32 | Club and general online play | USCF-style, many sites |
| 20 | Players rated under 2400 | FIDE standard |
| 10 | Masters, rating 2400 and above | FIDE elite |
FIDE rating regulations; USCF uses higher K for newer and lower-rated players. K controls how fast ratings move.
Common mistakes
- Swapping your rating and the opponent's — the sign of the gap flips the expected score.
- Using the wrong K-factor; a master moves about 10 points where a newcomer moves up to 40 for the same result.
- Expecting a big gain for beating a much weaker player; the expected score is near 1, so the reward is tiny.
- Reading the expected score as a pure win probability — with draws possible it is average points per game, not P(win).
Frequently asked questions
What is the Elo formula?
Expected score E = 1 / (1 + 10^((opponent − you)/400)). Your new rating is old rating + K × (actual result − E), where the result is 1, 0.5, or 0 for win, draw, or loss.
What K-factor should I use?
Use a higher K (32–40) for new or improving players so ratings settle quickly, and a lower K (10–20) for experienced or master-level players to keep them stable. Many casual systems just use 32.
Why do I gain more for beating a stronger player?
The expected score against a higher-rated opponent is low, so winning beats expectations by a lot. The gain is K times how far the result exceeded the expected score.
What does the expected score mean?
It is the average points you would earn per game against that opponent — 0.75 means roughly 75 percent of a point on average, blending wins and draws, not a flat win chance.
Is the 400 in the formula special?
It is a scaling constant chosen by Arpad Elo. It sets a 400-point gap to about a 10:1 expected-score ratio, defining what one rating point is worth.