How to Find a Percentage of a Percentage

Finding a percentage of a percentage means taking a slice of a slice. When you ask what is 15 percent of 20 percent, you are treating the 20 percent as the whole and finding 15 percent of it. The answer is not somewhere near 15 or 20 — it is much smaller, because you are shrinking an already small number.

This trips people up because both values are written with a percent sign, which makes them look like they belong on the same scale. In reality one of them is the amount and the other is the operation. Once you see 20 percent as the quantity being reduced, the calculation becomes ordinary multiplication.

Convert each percentage to a decimal by dividing by 100, multiply the two decimals, then convert the result back to a percentage by multiplying by 100. For 15 percent of 20 percent, that is 0.15 times 0.20, which equals 0.03, or 3 percent.

There is a faster shortcut you can do in your head. Multiply the two plain numbers and divide by 100: 15 times 20 is 300, and 300 divided by 100 is 3, giving you 3 percent directly. The shortcut works because dividing by 100 twice, once for each percentage, is the same as dividing by 100 once after multiplying.

The calculator handles the conversions for you and shows the full working so you can check it.

Stacked discounts are the classic example. An extra 15 percent off an item that is already marked 20 percent off is not 35 percent off — the second discount applies to the already reduced price, so the combined saving is less than the two added together. Percentage-of-a-percentage math tells you the real total.

It also shows up in commissions on fees, taxes on partial amounts, and survey results within a subgroup. If 40 percent of respondents own a car and 25 percent of those drive to work, then only 10 percent of everyone surveyed drives to work — 40 percent of 25 percent. Recognizing when a figure is a share of a share keeps you from overstating it.