How the Elo formula works
The Elo system first estimates each player's expected score. For player A against player B it is E = 1 / (1 + 10^((RB − RA) / 400)). Equal ratings give an expected score of 0.5; a 400-point rating gap gives the stronger player about a 91% expected score.
After the game, the rating change is ΔR = K × (S − E), where S is the actual score (1 for a win, 0.5 for a draw, 0 for a loss) and K is the K-factor. Beating an equal opponent with K = 32 gains exactly 16 points; upsetting a much stronger opponent gains more, while beating a much weaker one gains almost nothing.
The K-factor controls how fast ratings move: FIDE uses K = 40 for new players and juniors, K = 20 for established players under 2400, and K = 10 for elite players who have reached 2400. Many clubs and online platforms use K = 32 as their standard. Ratings between 100 and 3500 are supported here, which covers every practical chess rating.