Enter your rating and your opponent's to see your expected score and exactly how many points you'd gain or lose — per game and over a whole event — with FIDE (K=40/20/10), USCF (32/24/16) or a custom K-factor. Every result shows the formula with your numbers plugged in.
Up to 12 games. Games are processed in order and your rating is updated after each one, the same way federations process a rating period.
| Game | Opponent | Expected (E) | Result | Change | Rating after |
|---|
E is the score you're expected to get: 1 = certain win, 0.5 = even match, 0 = certain loss. A 400-point gap means ~0.91 vs ~0.09; 200 points ≈ 0.76 vs 0.24; equal ratings = 0.50 each.
S is your actual score (1 / 0.5 / 0). Score better than expected and you gain points; score worse and you lose them. K controls how fast the rating moves.
The live example above uses your inputs. In match play the two players' changes are equal and opposite, so points are conserved and ratings self-correct.
The K-factor is the multiplier that decides how quickly your rating moves: ΔR = K × (actual score − expected score). A high K means fast, volatile changes — appropriate for new players whose rating doesn't yet reflect their strength. A low K means slow, stable changes that protect established ratings. FIDE uses K=40 for players new to the rating list (and for juniors under 18 rated below 2300), K=20 for established players rated below 2400, and K=10 once a published rating reaches 2400. USCF ratings move on a similar scale (roughly 32 / 24 / 16 by rating band), and online platforms typically use somewhere between 10 and 40.
Expected score (E) is the fraction of a point a game is "worth" for you given the rating difference: E = 1 / (1 + 10^((R_opp − R_you) / 400)). If you're rated 1500 and face a 1650 opponent, E ≈ 0.30 — over many such games you'd score about 3 points out of 10. It's an expectation, not a pure win probability: E = 0.5 could mean ~50% wins, or fewer wins padded out by draws.
A single game moves your rating by at most K points, so meaningful movement takes several games. At K=20, beating an equal opponent gains about 10 points per game; going 4/5 against equal opposition gains roughly +30, while going 0/5 loses about −50. New players (K=40) converge to their true strength much faster — in roughly 30–50 games, which is exactly why FIDE gives them the higher K-factor. Established players' ratings drift slowly by design: a 2400+ player on K=10 needs to outperform expectation by a full point just to gain 10 points.
Because the formula only rewards and penalizes the difference from expectation. Against an opponent rated 200 points below you, your expected score is about 0.76, so a win earns just K × 0.24 (e.g. +4.8 at K=20) — you only get credit for outperforming what was already likely. But if you lose that game, the same gap works against you: K × (0 − 0.76) = −15.2 at K=20. The asymmetry cuts both ways: beating a higher-rated player pays more, and losing to a lower-rated player costs more. Over time this is what makes upsets "expensive" and keeps ratings honest.
Elo compares two players through a 400-point scale. A player 400 points above their opponent has an expected score of ~0.91 (roughly 10:1 odds of scoring); 200 points ahead ≈ 0.76; equal ratings = 0.50 each. After each game, the rating updates by K × (actual − expected): outperform the prediction and you gain, underperform and you lose. In a two-player match the changes are equal and opposite, so points are conserved, and because updates always pull results and ratings toward each other, the system self-corrects without any central authority re-rating anyone.
A performance rating is the rating your results would be worth: the level at which your score would have been exactly the expected score. The common approximation (used in the Performance tab) is TPR = average opponent rating + 400 × (2 × score% − 1). Score 50% against average-1650 opposition → TPR 1650; 70% → 1810; 30% → 1490. Federations compute official tournament performance ratings from a lookup table with similar values (and ±800 caps at perfect or zero scores), and title norms — the requirements for GM and IM titles — are defined in terms of performance ratings.