Percentage Calculator
The four percentage questions that actually come up, each with its own box.
Percentage Calculator
The Four Questions
Nearly every percentage problem is one of four shapes: what is X percent of Y, X is what percent of Y, what is the change from X to Y, and what was the original before a change. Mixing them up is what makes percentages feel harder than they are, so each has a separate field above rather than one box you have to reinterpret.
Increase and Decrease Are Not Symmetrical
This is the part that costs marks. Add 20 percent to 100 and you get 120. Take 20 percent off 120 and you get 96, not 100, because the second 20 percent is measured against a larger number. The two operations do not cancel out.
To undo a 20 percent rise you divide by 1.2, which is exactly what the reverse box does.
Percentage Points Are a Different Unit
If a rate moves from 5 percent to 7 percent, that is a rise of two percentage points, but a 40 percent increase in the rate itself. Both statements are true and they describe the same move. Saying which one you mean avoids an argument later.
Doing It in Your Head
Ten percent is a decimal point moved one place left. Five percent is half of that, and one percent is the point moved twice. Most everyday percentages can be assembled from those three: 17.5 percent is 10 plus 5 plus half of 5, which is quick enough to do while the calculator is still loading.