Percentages are a useful way of comparing how one part of something measures against the whole. For example, you might have a class in which 5 percent of the students are left-handed, or a household in which 75 percent of the children are girls. You can also use percentages to compare any two items that are related: for example, the price of a car last year versus the price of a car this year, or your grade on the latest test versus your grade on the test before. When you compare the percentages of two related items, you're actually measuring the percent difference or, depending on the context, the percent change.
Subtract the Two Values
Take the Absolute Value
Choose a Number
Divide by the Original
Multiply by 100
Subtract one of the values you're comparing from the other. The order of the values doesn't matter, but it's often easiest to subtract the smaller value from the larger. For example, imagine that you're finding the percent difference between the latest test, where you scored a 93 percent, versus a score of 82 percent on the test before. You could subtract thusly:
93 percent - 82 percent = 11 percent
Take the absolute value of your result from Step 1. Continuing the example, your result of 11 percent is already positive, so the absolute value is the same: 11 percent. But if you had swapped the order of your numbers while doing the subtraction, you might have ended up with a negative result:
82 percent - 93 percent = -11 percent
In this case, taking the absolute value of -11 percent gives you a result of (positive) 11 percent. This is why, for this calculation, the order of terms in subtraction does not matter.
Choose one of the numbers you started with to be the "original" number. This is the number you'll compare the difference, or amount of change, to. This will almost always be the first number in chronological terms. To continue the example, you'll choose the first of the two tests you took – the one where you scored 82 percent – as the "original" number.
Divide the amount of change (your result from Step 2) by the original number (which you chose in Step 3). Continuing the example, you have:
11 percent ÷ 82 percent = 0.1341
Multiply the result from Step 4 by 100 to convert it back into a percentage. The result is the percent difference, or the percentage change, between the two numbers you started with:
0.1341 × 100 = 13.41
So your test score changed 13.41 percent between the last two tests. But because you used an absolute value earlier in the process, you have to examine the original test scores to determine whether your score went up by 13.41 percent or down by 13.41 percent. In this case, since the second test score was higher than the first, your scores obviously went up by 13.41 percent. Good work!