Chess Elo Rating Change: How to Calculate the Points You Win or Lose
Your rating changes by K × (actual score − expected score). The expected score comes from the rating gap, and K is the factor your federation assigns: under FIDE rules 40 for new players and most juniors, 20 for established players below 2400, and 10 once you have reached 2400. A 1600 who beats an 1800 with K = 20 gains 15 points; losing the same game costs 5. This guide shows the formula, a full worked example and the K-factor rules.
What the Rating Change Is
The Elo system, devised by Arpad Elo and adopted by FIDE in 1970, assigns each player a number estimating their strength. After every rated game the number moves up or down according to how the result compared with what the ratings predicted. Rating is the currency of competitive chess: it sets tournament seedings, title norms, eligibility for rating-restricted sections and, informally, bragging rights. A single game is noisy, but each adjustment nudges the rating toward the player's true strength.
Expected Score and the K-Factor
Expected score is the result the ratings predict, between 0 and 1, computed from the rating difference:
Expected = 1 ÷ (1 + 10^((opponent rating − your rating) ÷ 400))
Equal ratings give exactly 0.5. The 400 sets the scale: a 400-point advantage gives an expected score of about 0.91 (1 ÷ (1 + 10⁻¹)). For players rated below 2650, FIDE caps the difference used in the calculation at 400 points, so a gap of 600 counts as 400. The Chess Expected Score Calculator applies this formula and multiplies by a number of games to give the points you should expect from a match or event.
The K-factor is the most points one game can move your rating. FIDE's rating regulations (in force since March 2024) use K = 40 for a player with fewer than 30 rated games, and for players under 18 as long as their rating stays below 2300; K = 20 for players rated below 2400; and K = 10 once a player's published rating has reached 2400, permanently. A high K lets a new rating find its level quickly; a low K protects an established rating from the randomness of individual games.
How to Calculate the Rating Change
Rating change = K × (actual score − expected score)
The actual score is 1 for a win, 0.5 for a draw and 0 for a loss.
Worked example. You are rated 1600, your opponent 1800, you win, and your K-factor is 20.
1. Rating gap: 1800 − 1600 = 200 in the opponent's favor
2. Exponent: 200 ÷ 400 = 0.5, and 10^0.5 ≈ 3.162
3. Expected score: 1 ÷ (1 + 3.162) = 1 ÷ 4.162 ≈ 0.240
4. Change: 20 × (1 − 0.240) = 20 × 0.760 = 15.2, so +15 points
Your rating becomes 1615 and your opponent's falls by the same amount (with the same K; if the opponent's K differs, their change differs too). Lose the same game and the change is 20 × (0 − 0.240) = −4.8, rounding to −5: a small penalty for an expected result. That asymmetry is the heart of Elo. Beating a favorite is worth far more than losing to one costs, and a draw against a higher-rated player is still a gain because your expected score was below 0.5.
The Chess Elo Rating Change Calculator takes both ratings, the result and a K-factor and returns the change rounded to a whole point; it opens on this example (1600 beats 1800 at K = 20, +15) and applies FIDE's 400-point cap. Its K-factor menu includes FIDE's 40, 20 and 10 alongside 32, 24 and 16, which other federations and online platforms use, so pick the one your rating system actually applies. FIDE itself computes each game's change to one decimal and sums them over an event before rounding.
Using the Numbers
Playing up against stronger opposition is low-risk and high-reward; playing down is the reverse, since a win barely registers while an upset loss stings. Knowing the stakes of a pairing in advance helps you judge which events are worth entering. After an event, a tournament performance rating runs the same logistic curve in reverse, estimating the rating level you played at from your average opponent rating and score percentage.
Common Mistakes
Assuming a win is always worth the same. The value depends entirely on the rating gap.
Using the wrong K. A junior on K = 40 moves twice as far as an established player on K = 20 for the identical game.
Using post-event ratings. The ratings in force before the game (the published list at the start of the event) are the ones that count.
Expecting one game to reveal your strength. Elo converges over many games; a single result is one small nudge.
Related guide: Swiss Tournament Points: How to Calculate the Score You Still Need.