The formula (one line)
Elo change is usually modeled as Δ = K × (S − E). The only “hard” part is understanding expected score (E) and picking the right K.
Example 1: equal ratings
If you’re 1500 and your opponent is 1500, your expected score is ~0.50. With K=20, a win is roughly +10 and a loss is roughly −10.
Example 2: upset win
If you’re 1500 and your opponent is 1700, your expected score is low. So if you win, you gain more than in the equal-rating case.
Example 3: why platforms differ
FIDE/USCF/Lichess/Chess.com can use different K-factors, provisional rules, floors, and sometimes different systems. Treat calculators as an estimate, not a legal contract.
Try the tool
Use the interactive version here: Elo Gain/Loss Calculator
If you want the concepts first: What is Elo in chess?