How this number is made
Percent means per hundred. The three questions on this page are the ones people actually type into a search box: a slice of a number, a number as a share of another, and the change between two numbers. They are not the same operation.
- “What is X% of Y?” multiplies Y by X ÷ 100.
- “X is what percent of Y?” divides X by Y. Y cannot be zero.
- Percent change divides the difference by the starting number, not the ending one.
Formula
Percent of: (X ÷ 100) × Y. Ratio: (X ÷ Y) × 100. Change: ((B − A) ÷ A) × 100.
Worked example
18% of 240 is 43.2. 43.2 is 18% of 240. A move from 240 to 283.2 is an 18% increase. A move from 283.2 back to 240 is a 15.25% decrease, because the starting number changed.
Questions
Why isn’t a 20% drop followed by a 20% rise back to the start?
The second 20% applies to the smaller number. Twenty percent off 100 is 80. Twenty percent of 80 is 16, which only gets you to 96.
Can I use this for a price or a raise?
Yes, if you know which question you are asking. A raise from $20 to $23 an hour is percent change. A $42 fee on a $240 bill is the ratio question.