🎯

Chess Rating Change (Elo) Calculator

See how many rating points a game will win or lose: enter your rating, your opponent's rating, the result and your K-factor to get the exact Elo change and new rating.

Your rating

Opponent rating

Result

K-factor

Loading calculator…

How it works

expected score E = 1 ÷ (1 + 10^((opp − you) ÷ 400)) · rating change = K × (actual score − E) · new rating = old rating + change

The Elo system rates the difference between two players by how surprising a result is. Your expected score against an opponent is a smooth function of the rating gap: 400 points of advantage means you are expected to score about 0.91, level ratings means 0.5. After the game your rating moves by the K-factor times the gap between what you actually scored and what was expected — beat a higher-rated player and you gain a lot; lose to a much weaker one and you drop hard. The K-factor sets how twitchy the rating is: high for new or junior players so they reach their true level fast, low for established masters so their rating is stable.

Worked example

Rated 1500 against a 1600, your expected score is 1 ÷ (1 + 10^((1600 − 1500) ÷ 400)) = 1 ÷ (1 + 10^0.25) ≈ 0.36. Winning (actual score 1) with K = 20 gives a change of 20 × (1 − 0.36) = +12.8 points, taking you to about 1513.

Sources: Elo rating system (Wikipedia)

Frequently asked questions

What K-factor should I use?

FIDE uses 40 for a player's first games and juniors, 20 for most established players under 2400, and 10 once a player reaches 2400. Online sites set their own — chess.com and Lichess use larger, provisional K-factors that shrink as you play more.

Why do I gain more for beating a stronger player?

Because the result is more surprising. Your expected score against a stronger opponent is low, so actually scoring 1 creates a big gap between actual and expected — and the rating change is proportional to that gap.

Does a draw ever change my rating?

Yes, unless you and your opponent are exactly equal. A draw is worth 0.5; if your expected score was above 0.5 you lose a few points, and if it was below 0.5 you gain a few.

Related calculators

Elo Rating Calculator

See your new Elo rating after a game: the expected score from the rating gap, the points won or lost, and how the K-factor scales it.

Dice Probability Calculator

Exact dice odds for any NdS roll: the chance the total is exactly, at least, at most or between targets, with a modifier, D&D advantage or disadvantage, keep-highest or keep-lowest (4d6 drop lowest), rerolls, and counting successes in a dice pool — plus the full distribution table and chart, mean and standard deviation.

RPG XP-to-Level Calculator

Work out the experience points needed to reach your next level or a target level on a custom XP curve — plus XP for the next level and levels remaining.

Expected Value Calculator

Compute the expected value of a discrete probability distribution from its outcomes and probabilities — with the variance and standard deviation.

This calculator is for educational purposes. Double-check important results before acting on them.