Percentage of a number and percentage change

Three modes and when to use each

“Percent of a number” answers the question “how much will that be”: 15% of 2400 is a shop discount or a tax on an amount. “Share of one number in another” is used when you know that 120 out of 800 is what percentage: this is how plan completion, defect rate and conversion are calculated.

“Percentage change” shows the growth or decline between two values: it was 2400, it became 3000 — plus 25%. This mode is most often confused with percentage points, which is what applies to rates and inflation.

How to calculate by hand

Percent of a number: multiply the number by the percent and divide by 100. Share: divide the part by the whole and multiply by 100. Change: divide the difference by the original value and multiply by 100. In all three cases what matters is the base the percentage is calculated from: 20% of 1000 and 20% of 800 are different amounts.

Percentages and percentage points

The rate rose from 20% to 25% — that is 5 percentage points, but 25% relative growth. If a bank says “the rate rose by 5%”, clarify what is meant: points or relative change. The difference in these wordings sometimes costs money.

A negative result in the change mode means a decrease. For example, −20% is a drop by one fifth, not a “minus twenty” increase.