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Elo Rating Calculator

Find the pre-game win probability the Elo rating system predicts for two players, and the resulting rating change after a win, draw, or loss.

Pre-game win probability
50%
Opponent's pre-game win probability
50%
Rating change
16
New rating
1,516

How it works

The Elo rating system estimates a player's pre-game win probability from the gap between the two ratings: expected score = 1 ÷ (1 + 10^((opponent's rating − player's rating) ÷ 400)). The scale is built so that a 400-point rating advantage makes a player exactly ten times as likely to win as to lose — the same formula chess federations, many esports ladders, and sports analytics sites use.

After the result is known, the rating updates by how much better or worse the outcome was than predicted, scaled by the K-factor: new rating = old rating + K × (actual score − expected score), where actual score is 1 for a win, 0.5 for a draw, and 0 for a loss. A favorite who wins as expected gains only a little; an underdog who pulls off an upset gains much more, because the formula only rewards results that beat the prediction — even a loss to a much stronger opponent can cost very few points, since it was close to what the ratings already predicted.

K controls how fast ratings react to new results: a higher K (commonly 32 for less-established players) makes each game move the rating further; a lower K (commonly 10-16 for top-tier players with a long history) makes ratings more stable game to game.

FAQ

Why did my rating barely change even though I won?

Elo only rewards a result relative to what was predicted. If you were already a heavy favorite, the system expected you to win, so beating a much weaker opponent confirms the prediction rather than revising it — the rating change shrinks toward zero as your pre-game win probability approaches 100%. A genuine upset moves the rating much further, in either direction.

What K-factor should I use?

There's no universally 'correct' value — it's a trade-off between responsiveness and stability that different organizations set by policy. Chess federations commonly use a higher K (around 32 or 40) for newer or lower-rated players whose true strength is still uncertain, and a lower K (around 10-16) for established top players, so a single unlucky result doesn't swing a well-established rating too far.

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