A percent is a piece of something, a chance, average, or even a way in which to work out your grades in school. In essence, a percentage or percent is something that can exist in almost any situation. You can eat 50 percent of your sandwich at lunch, have a tiny sliver of a chance of winning the lottery, or even pay a rate of interest on money you borrow from the bank.
You can also see percentages written and printed everywhere in different forms. These include: percent, per cent, %, and pct. One percent is equal to one-hundredth of something. So, if you had three parts out of 100 of something, you would have three percent, 3%, 0.03, three hundredths, or 3/100.
Does that sound confusing? It doesn’t have to be. In essence, you use percentages to determine the size of a number compared to another. You can work it out by hand or even use a percentage calculator.
An example of how percentages work:
You have one large pumpkin pie that mom made for Thanksgiving. Dad said you’re allowed 20 percent of the dessert – or 20 hundredths of it which is already in six pieces. You need to then divide the pie into 100 pieces, with 20 parts of that now mutilated pie belonging to you.
20/100 x 6 = 1.2
20 percent of six pieces is 1.2 slices of pie
A percentage is also something you use to connect two numbers as a fraction of 100. The goal is to find out how the two numbers relate.
For example, let’s say that a number labeled ‘A’ is 25 percent of B, then A to B is 25 to 100. As A is four times smaller than B, it’s also one to four.
If you want the percentage of something, then it’s always easier to put it into a visual concept. Let’s say you have 100 pieces of candy. Each candy represents one percent of the total amount or one hundredth.
If you wanted to know the percentage of three pieces of candy, then it would be three percent, as each bit represents one percent.
Or, how about if we had 300 pieces of candy, all individually wrapped but set out together in groups of three. You know that now, one percent of 300 pieces of candy is three. What if you wanted to find out 20 percent? That equals 20 lots of three bits of candy = 60 pieces in total.
What if you had 250 pieces of candy, with each set containing two pieces of candy, but with 50 left over? You then have to spread those remaining candy over each set of two. You would have to cut each piece of candy in half so that each group could have two and a half bits.
It might seem tricky, but a percentage calculator can help you to work out these figures quickly!
Percentages are not only good for working out how much candy to give your friends but determining other things too. They are all about comparing one figure to another. Let’s say you had to do a few tests at school. You had two tests where you got 75 out of 100 and 139 out of 200. It can be hard to understand how well you did without turning it into a percentage.
You would have to determine the percentage of 75 out of 100 and 139 out of 200.
75 / 100 = 0.75 (x 100 to get 75 percent)
139 / 200 = 0.695 (x 100 to get 69 percent)
As you can see, even though the numbers were higher on the last test, you actually did better on your first one. You can also see that you can turn percentages into decimals and vice versa, with 0.75 the same as 75 percent.
In most cases, a percentage calculator is going to be your first port of call for learning how to find the percentage of a number. However, for whatever reason you can’t access it, it’s helpful to understand how to calculate it by hand or in your head.
As we now know, a percentage relates one number to another – A and B. Let’s say there is a group of six people, with three boys in the group and three girls. What’s the percentage of boys to girls?
Three out of six, or 3/6 are boys. The number 3 is the numerator, and 6 is the denominator. These form two parts of a fraction.
If you were to calculator the percentage, you would take this fraction then multiply it by 100 with a % sign at the end.
100 x 3 / 6 = 50%
Fifty percent (50%) of the group consists of boys, and you now know how to convert between percentages and decimal fractions!
However, what if you don’t know the numerator, and only know that there are 60% chocolates in a box, with six chocolates altogether?
We know the formula is 100 x numerator/denominator = percentage, but we don’t know what the numerator is. We do, however, have other information.
Divide both sides of the equation by 100, then multiply them by the denominator.
Numerator = percentage x denominator / 100
Add the values we know so far.
Numerator = 60 x 6 / 100
Numerator = 3.6 chocolates
What if you don’t know the denominator? Let’s say you spent 40% of your pay on rent, which ended up being $400. You now know that $400 was 40% of your income.
100 x numerator / denominator = percentage
100 x 400 / denominator = 40
Multiply both sides by the denominator before dividing it by your percentage.
100 x 400 / 40 = $1,000
Most percentage-related problems will have three parts, and we will work these out using pieces of candy. You know the percentage of candy, how much candy you have in total, and the part of the candy. These three components come with three formulas.
1. Percentage formula
Percentage = 100 x the part / the whole
2. Part formula
Part = the whole x the percentage / 100
3. Whole formula
Whole = 100 x the part / the percentage
Calculating percentages is something everyone will need to do at some part in their life. Learning how to use a calculator tool now can save a whole lot of grief in the future.
Forms of calculations have been around since ancient times, with Romans using Roman numerals such as I, V, X, and L. People would also calculate in fractions of 100, with them becoming more commonplace with the introduction of the decimal system.
In everyday life, we apply many formulas and techniques from all those years ago, but the percentage sign is something that’s relatively new – being evolved and fine-tuned over the years.
Most people believe that percent means per centum in Latin, which means “by a hundred.” In reality, it’s Italian for per cento, meaning “for a hundred.” Per cento became shortened in form over several hundred years until the cento part of the word became two circles, and the line became the divisional component.
The percent symbol is now also used in programming languages and modulo operations. It also helps to determine the relative error between an observed and real value in a measurement. There are also percentage signs that look a little funny. One with an additional circle (‰) means per 1,000 instead of per 100, while ‱ is per 10,000. You can learn more about these below.
If you think that percentages only relate to a hundred parts of something, then think again! Per mille or ‰, is one-thousandth of something = 1/1000 or 0.001. Let’s say you purchased a car for $12,000 and wanted to spend 1 ‰ of that on fuel; you would be filling your tank with $120 of gas.
If, however, you wanted to use the percentage calculator to figure that out, you could use numbers that were ten times lower.
A basis point is ‱ or one ten thousandths. It’s ten times smaller than per mille, so when you use the percentage calculator, you will divide the figure by 100.
Percentage points, which people often refer to incorrectly as percent points, are something we use in everyday life but may not realize it. Percentage points are where you change from one percentage to another and want to know that difference.
For example, let’s say a well-known politician polled at 10 percent. Since then, he saved a baby from a speeding car and now 22 percent of the population are offering him their vote. You may think that it’s a 12 percent increase, but that’s not right.
Instead, let’s say there are 1,500 people in the politician’s area, and initially, 10 percent wanted to vote for him = 150 people. However, 22 percent of 1,500 is 330 people which would not make any sense. That’s why percentage points are convenient to change from one percentage to another. A change from 10 percent to 22 percent is 12 percentage points or 120 percent.
You can also look at percentage points from another perspective where percentage points change is the previous value and its relation to the new value. The first value is 10 percent, which means that one percent of 10 percent is 0.1 percent.
It can also refer to the whole part – the 1,500 population and subtracting one percentage from another. E.g. 22 percent – 10 percent = 12 percent.
Whether you use per cent or percent depends on from where you originate. As you know, the United Kingdom and American English differ in some words, and percent is one of them. If you live in the United States, it’s one word. If you live in the United Kingdom, it’s two.
