How this calculator works
Elo compares two ratings through the expected score. A 400-point advantage means the stronger player is expected to score about ten times as often as the weaker one, or roughly 0.91 in a win-loss format. After a game, the new rating is the old rating plus K times the difference between the actual score and the expected score. A surprise result moves the rating more than an expected one. In a tournament, each game is processed in order, so the rating entering the next game is the result of the previous one.
Formula
Expected score = 1 / (1 + 10^((opponent rating - your rating) / 400)). New rating = old rating + K x (actual score - expected score). A win scores 1, a draw 0.5 and a loss 0. The tournament table applies the same step sequentially.
Worked example
A 1500 player meets another 1500 player with K = 30. The expected score is 0.5. A win gives 1500 + 30 x 0.5 = 1515, a draw leaves the rating at 1500, and a loss gives 1485. If the next game is against 1600 and ends in a draw, the expected score from 1515 is 0.38, so the draw adds 30 x 0.12 and takes the rating to about 1518.6.
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Frequently asked questions
What K factor should I use?
Chess federations use different values by rating and age. Common values are 40 for new or junior players, 20 for established players and 10 for very strong players. The right choice depends on the rules of your competition.
Why is the expected score not a win probability?
It is the expected result in points. A 0.75 expected score could come from a high chance of a win plus a draw, not from a 75 percent chance of winning. In a win-only format the numbers coincide, but with draws they do not.
What happens after many games?
The rating converges toward the level implied by results. The K factor controls how quickly it gets there: a large K reacts strongly to each game, while a small K is more stable.
Can I use Elo for team sports?
The same arithmetic applies to teams or players, but the rating is only as meaningful as the opponent pool and the rules for who plays whom. Team sports often add home advantage and margin-of-victory adjustments that this page does not model.