This handles the three common percentage questions: a percent of a number, what percent one value is of another, and the change between two values.

The three percentage questions

Almost every percentage problem is one of three questions in disguise. The first finds a part of a whole, as in twenty percent of eighty. The second expresses one number as a percentage of another, as in twenty out of eighty. The third measures change over time, as in a price moving from eighty to one hundred.

Confusing these three is the most common percentage mistake. A discount uses the first form, a test score uses the second, and inflation or growth uses the third, yet they all get described loosely as percentages in everyday speech.

Percent change has a quirk worth remembering. A fifty percent drop followed by a fifty percent rise does not return to the starting value, because the second percentage is taken from a smaller base. This single fact explains many misleading statistics.

The formula

Worked example

20% of 80 = (20 / 100) x 80 = 16. And 20 is (20 / 80) x 100 = 25% of 80.

How to read your result

Percent change is positive for an increase and negative for a decrease. Be careful: a 50% drop then a 50% rise does not return to the start.

Frequently asked questions

What is the difference between the three modes?

One finds part of a whole, one finds the ratio as a percent, and one measures change over time.

Why use absolute value for change?

So a change from a negative starting value still reports a sensible direction.

Can percentages be over 100%?

Yes - any time the part is larger than the whole, or the value more than doubles.

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