Percentage Calculator

Almost every percentage problem is one of three: what is X percent of Y, X is what percent of Y, and what is the percentage change from X to Y. The first two are straightforward. The third is where errors cluster, because percentage change is always relative to the starting value, and people routinely compute it against the wrong one. A rise from 40 to 50 is a 25 percent increase; a fall from 50 to 40 is a 20 percent decrease. Same ten units, different denominators, different answers, and neither is a rounding artefact.

That asymmetry is why percentage changes do not cancel out. A 20 percent fall followed by a 20 percent rise does not return to the starting value: 100 becomes 80, and 80 plus 20 percent is 96. The gap widens as the percentages grow, which is the arithmetic behind why a portfolio that halves needs to double to recover rather than gaining another fifty percent. Any time two percentage changes are applied in sequence, they multiply rather than add.

The last distinction worth holding onto is percent versus percentage point. If an interest rate moves from 4 percent to 5 percent, that is a one percentage point rise and a twenty-five percent increase, and both statements are true. Reporting mixes them constantly, usually in whichever direction makes the number sound larger. When a figure matters, check which of the two is being quoted before drawing a conclusion from its size.