The formula
expected = 1 ÷ (1 + 10^((opponent − yours) ÷ 400)) · new = rating + K × (result − expected)
Where it comes from
The system does not reward winning but winning by more than expected. First it works out how much you are expected to score from the rating difference, then it adds the gap between what you actually did and what was expected, multiplied by a K factor. Every 400 points of advantage means ten times the chance of winning.
How to work it out by hand
- Subtract your rating from the opponent's and divide by 400
- Raise 10 to that number, add 1 and take the inverse: that is your expected score
- Subtract the expected score from the actual result (1 win, 0.5 draw, 0 loss)
- Multiply by K and add it to your rating
What is worth knowing
The K factor decides how far the rating moves: FIDE uses 40 for new players, 20 in general and 10 for anyone past 2400, so that established ratings do not swing on a single game. The system is zero-sum: what one player gains the other loses exactly. And the most useful practical consequence is that losing to someone much weaker costs far more points than beating them gains.