Percentages fill our daily lives, but if you have trouble calculating them in your head, you might be missing some key tricks that can make your life a lot easier.
To understand the mental calculations, we’ll start with a basic review of what percentages are and how to calculate them when you’ve got the right tools. Then we’ll teach you some tips and tricks, along with the math behind the concept of “increasing by a percent.”
Confused? Don’t worry—we’ll break it down for you. Here’s how to start calculating percentages like a pro:
The Basic Process of Calculating Percentages
If you want the most straightforward way to calculate percentages, and you have a pen and paper, a calculator, or something with a calculator function handy, here’s what to do:
The first thing to understand is that “percent” comes from a phrase meaning “by the hundred.” So you’ll have to divide whatever number comes in front of the word “percent” by one hundred to get its true value. This means 40 percent, or 40%, actually means 0.40, and 100 percent means 1.
Then, all you have to do is multiply this value to whatever you’re taking the percentage of. If you need to figure out 40 percent of 75, you should multiply 0.40 by 75 to get your answer. And if you did the math right, you should come up with an answer of 30—that is, 40 percent of 75 is 30.
The 10 Percent Shortcut
What if you don’t have a calculator handy, though? Here’s a shortcut that can help you figure out lots of everyday situations, like discounts and tips.
Divide by 10
Let’s say you want to tip a restaurant server 20 percent of a $15 bill. You can start by dividing the bill by 10, which you should be able to do in your head. All you need to do is move the decimal point one spot over.
In this case, 10 percent of your bill is $1.50. We’ve just moved the decimal point one spot to the left.
Multiply by the Right Multiple of 10
But you’re not done yet. You want to calculate 20 percent, not 10 percent of the bill. So what you have to do is multiple your 10 percent number by the appropriate multiple.
20 percent is 2 times 10 percent, right? So if we already know that 10 percent of the bill is $1.50, we can figure out that 2 times that number is $3. And that’s your final number—go ahead and tip your server $3.
If you’re in a situation where you need to figure out a certain percentage off an amount, you have a couple of choices. You could go through all the steps above and subtract it from the original amount after.
Or you could subtract in the beginning. So if you want to know the price of a sweater that’s 30 percent off, you could start by realizing that what you really want to know is what 70 percent of the original price is. That’s 100 percent minus 30 percent.
This way, you won’t have to do a messy subtraction at the end.
The Fractions Shortcut
This is one you probably already do, at least for the big one-half fraction. When you see that something is 50 percent off, you’ll recognize that 50 percent is the same thing as one half, meaning all you need to do is divide that number by 2.
50 percent of 10 is 5, 50 percent of 800 is 400, and so on. But did you realize you can do this for more than just the one-half fraction?
What to Remember
Some basic fractions to keep in mind are:
- One-half = 50 percent
- One-third = 33.33… percent (this is a repeating number, meaning it will keep repeating the digit 3 forever, so let’s round it to 33.3 percent)
- One-quarter = 25 percent
- One-fifth = 20 percent
So if we want to know what 25 percent of 8 is, we can remember that 25 percent is the same thing as one-quarter. One-quarter of 8 is 8 divided by 4, which is 2.
Going a Step Further
Now that you have these basic conversions, you can use these to figure out multiples of those fractions. For example, if you want to know what 40 percent of something is, you might recognize that this is a multiple of one of the fractions above.
Here’s how to figure it out from there:
We can start by realizing that 40 percent is 2 x 20 percent.
We already know that 20 percent means one fifth, so 40 percent must be two fifths. If the number we’re dealing with is easily divisible by 5, the rest should follow pretty smoothly:
Let’s say we want to know what 40 percent of $25 is. We’re taking the fractions shortcut and have realized that 40 percent just means two fifths. So what’s one-fifth of $25?
$5! And two of these fifths is just 2 x $5, which is $10. So 40 percent of $25 is $10.
Increasing by a Certain Percent
Sometimes percentages give off a different impression than putting things in terms of multiples. For example, instead of saying, “We doubled our revenue last quarter,” someone might say, “Our revenue increased by 100 percent.” Though these might feel a bit different, they mean the same thing.
You could figure out percent increases or decreases with some tech help, especially if you’re calculating lots of numbers at once. For a guide on that, go here: https://setapp.com/how-to/how-to-calculate-percentages. But here are the basics if you’re doing it on your own:
Let’s See an Example
When people talk about things increasing by a certain percent, they’re using a certain number as a reference—for example, the revenue from last quarter, which might be $3,000. Then they’ll compare the increased amount to that reference number. Let’s say they made $5,000 this quarter, meaning there was an increase of $2,000.
Now, what they’ll need to do is figure out what percentage the increase ($2,000) is of the reference ($3,000). We’ll have to do a bit of math to follow along here:
- $2,000 is what percentage of $3,000?
- $2,000 = P% × $3,000
- $2,000 = P/100 × $3,000
At this point, you can group the items on the right however you want, because they’re all related by either multiplication or division.
- $2,000 = ($3,000 x P)/100
- $200,000 = $3,000 x P
- $200,000/$3,000 = P
- P = 66.66…
This is a repeating number, so let’s round it up to 66.7 percent. So the revenue increased by 66.7 percent.
Checking the Answer
Just to check that this makes sense, let’s verify that the increase ($2,000) really is 66.7 percent of the revenue from last quarter ($3,000):
- $2,000 = 66.7 percent of $3,000
- $2,000 = 66.7/100 x $3,000
- $2,000 = 0.667 x $3,000
- $2,000 = $2,001?
We’re $1 off here, but remember that 66.7 percent was a rounded number, not an exact one. This explains the $1 difference.
Can You Calculate How Much You’ve Learned Just Now?
Whether your math skills are historically iffy or you know math but not the everyday tricks, we hope you learned something new in this guide. Next time you see a discount, a bill, or a financial report, or simply the RTP of a slot machine, you can put those percentage skills to work!
Calculating percentages is just one of the many tips we have to offer. For more, check out the rest of our site!