Elo rating change calculator
Elo turns a rating gap into a win probability, then moves both ratings by the surprise in the result.
New rating
1614.1
- Rating change
- 14.07
- Expected score
- 0.296 61
- Win probability
- 29.66 %
- Opponent new rating
- 1735.9
- Most you could gain
- 14.07
- Most you could lose
- 5.93
Show the working
- Your rating = 1600
- Opponent rating = 1750
- Result = 1
- K-factor = 20
- diff = 1750 - 1600 = 150
- Expected score = 1 / (1 + 10^(150/400)) = 0.296 615
- Rating change = 20 * (1 - 0.296 615) = 14.0677
- New rating = 1600 + 14.0677 = 1614.07
- Opponent new rating = 1750 - 14.0677 = 1735.93
- Win probability = 0.296 615 * 100 = 29.6615
- Most you could gain = 20 * (1 - 0.296 615) = 14.0677
- Most you could lose = 20 * 0.296 615 = 5.9323
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- expected score = 1 / (1 + 10^((opponent - you)/400))
- new rating = old + K x (result - expected)
A 400-point gap gives the stronger player a 10-to-1 expected score, which is where the 400 in the formula comes from.
FIDE uses K = 40 for new players, 20 for most, and 10 above 2400.