Update a player’s Elo rating after a single game, using the same rating system chess federations, esports leagues, and many competitive rankings run on.
How it works
Elo first computes an expected score from the two ratings: Expected = 1 ÷ (1 + 10^((Opponent Rating − Your Rating) ÷ 400)), then updates the rating based on the actual result: New Rating = Old Rating + K × (Actual Score − Expected Score), where a win scores 1, a draw scores 0.5, and a loss scores 0. Two 1500-rated players who draw see no rating change; a 1500 beating another 1500 with K=32 gains 16 points.
What this does not include
This calculates a single game’s rating update using a fixed K-factor you supply — it doesn’t model rating decay, provisional-rating rules, or the different K-factors some organizations apply to new or highly-rated players.
How to use this calculator
- Enter your current rating and your opponent’s rating.
- Select the result (win, draw, or loss).
- Enter the K-factor (32 is a commonly used default).
A worked example
Two 1500-rated players, K=32: a win gives an expected score of 0.5 (evenly matched), and the winner’s new rating becomes 1500 + 32 × (1 − 0.5) = 1516.
A 1400-rated player beats a 1600-rated opponent, K=32: expected score was only 0.2403 (the underdog was unlikely to win), so the rating jumps further — to 1424.3119 — since beating a stronger opponent moves the rating more than beating an equal one.
What the variables mean
| Variable | Meaning |
|---|---|
| Rating, opponent rating | Current Elo ratings entering the game |
| Expected score | Win probability implied by the rating gap, before the game is played |
| K-factor | How much a single result can move the rating |
Edge cases worth knowing
An upset win moves the rating more than an expected win does. Beating a much stronger opponent (low expected score) produces a bigger rating jump than beating an evenly matched one, since the actual result diverged further from what was predicted.
A draw between equally rated players changes nothing. Expected score is 0.5, actual score is 0.5 — the update term (actual − expected) is zero.
What does the K-factor control?
K-factor sets how much a single game can move a rating — a higher K makes ratings react faster to recent results but also makes them noisier.
Why 400 in the expected-score formula?
400 rating points corresponds to roughly a 10-to-1 favorite in the original Elo formulation — it sets the scale of how much a rating gap translates into win probability.
Who invented the Elo rating system?
Physicist Arpad Elo developed it for chess rating in the 1960s; it’s since been adopted by many other competitive games and sports for ranking players.
