What is a percent?

A percent is a number that expresses a ratio in terms of 100.

Percentages and Ratios (and Fractions too)

Okay. Great. What does THAT mean?

Well, a ratio is a relationship between two numbers. If a math class has 12 boys and 15 girls, we would say the ratio of boys to girls is 12:15. (We could also say the ratio of girls to boys is 15:12.) And just an FYI, we could also write the ratio of boys to girls this way: 12/15.

Wait a minute, that last thing is a fraction!

Yup, the same thing. A ratio is the same thing as a fraction; it's just written out differently.

Alright, that's what a ratio is, but what does "in terms of 100" mean?

That's the really vital part. "In terms of 100" means, if the right-hand side of the expression "12:15" (the "15") were actually "100" what number would we use to replace the "12" so we can still maintain the ratio of 12:15?

The answer is "80". We can say that the ratio 12:15 is the same as 80:100 or 80%. That is, the class has 80% the number of boys has it has girls. Can you figure out which of the below percent calculators I used to come up with this answer? If not, don't worry. Just stay tuned.

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Original Size
Percentage Calculator 1

This Number is "X" Percent Of What Number?

Percentage Calculator 2

What Number Is "X" Percent Of This Number?

Percentage Calculator 3

Percent Increase/Decrease Calculator

Percentage Calculator 4

If I want to know what percentage of the class is made up of boys, I would still use the same calculator, but the ratio is no longer 12:15, but rather it is 12:27. Why?

Because to know the percentage of boys in the class, we need to write the ratio as the number of boys to the total number of students in the class. So the first ratio (12:15) is the number of boys relative to the number of girls and the second ratio (12:27) is the number of boys relative to the entire class size.

Percentages Are Normalized Ratios

This is all well and good. But why would I want to take a perfectly good ratio of 12:15 or 12:27 and in essence convert the right side to 100?

Percents give us a way to accurately compare two or more relationships incorporating different sizes or amounts.

For example, you just received the results of a math test, and you got 45 right answers out of a total of 52 questions. Your friend gets a back a science test, and she got 39 questions right out of 44. Who did better? Scroll up to percentage calculator 1 to find the answer. And now you know what calculator I used to normalize the above 12:15 ratio to a percent.

Normalize is just a fancy word meaning to make the same. When you convert a ratio to a percent, it can be said that you are normalizing the ratio. And we normalize the ratios to compare results.

Percentage Calculator

Calculator 1 converts any ratio to a percent. That is, it answers the question "what percent is 'X' of 'Y', i.e., 'X:Y' or 'X/Y'"?

To use it, first understand the ratio. For example, if you earn \$1,000 a week and you have \$183 taken out of your pay, and you want to know what percentage of your pay gets deducted from the total then the ratio you want to convert is 183:1000. Enter 183 as "This number" and the 1,000 as the "is what percent of this number." The result is 18.3%. Or you have 18.3% deducted from your pay.

Calculator 1 can also be used as a fraction to percent calculator. How? If you've been following along, you probably already know. But for those who may have skipped ahead, the answer is simple. Take any fractions, for example, "27/82", and enter the numerator (27) into "This number." Then take the denominator (82) and enter it into "is what percent of this number." The percentage is 32.9268%.

Notice also that percentage calculator 1 works as a percent to decimal calculator as well.

Are you getting the idea?

Do you see the relationship between percents, ratios, and fractions?

If not, this would be a good place to stop and review what I've written so far. The balance of the material builds on what we've learned. Go ahead, and I'll wait.

Other Calculations Involving Percentages

What happens when we know the percent, but we don't know one of the two numbers in the ratio?

1. Imagine we want to know "X" is 20% of what number "Y" if "X" equals 2,250. (The ratio looks like this: 2250:Y). You have to pay 20% of an upcoming doctor's bill, and the insurance company will pay the balance. You have \$2,250. What is the maximum amount the bill can be so that you'll still have enough to cover your share? Use Percentage Calculator 2
2. Or suppose we want to know what number "X" is 90% of "Y" if "Y" is 145? (The ratio looks like this: X:145). An "A" grade is 90% or above. If there are 145 questions on the test, how many do I have to get right to get an "A"? Use Percentage Calculator 3
1. Finally, what if you need to know the percentage change (increase or decrease) between amount or size "X" and "Y"? An item you have been thinking of purchasing had cost \$249.95 and now costs \$199.95. The ratio is 249.95:199.95. What is the percent the price dropped? (We would ask what is the "discount?") We can easily flip the calculation on its head. Suppose the price had been \$199.95 and is now \$249.95 (199.95:249.95), what is the percent increase? Use Percentage Calculator 4

Why do the above two calculations have different results?

Notice ratios need not have only integer (whole number) parts. Frequently, many people need to do percentage calculations involving money, as we see above.

Join the conversation. Tell me what you think.
• melinasays:

how do you find the increase and deacrese in numbers ike percentages

• Ed Hinsleysays:

How can I find the percentage of 2066 to 117252 please?

• Karlsays:

Please use the 3rd one down. The “What Percent Of Calculator”.

• alex linsays:

third one down the calculator

• alex linsays:

noice!hallelujah!

homework solved!

• juliesays:

how can I find the percentage of this 17.25% of 14102.93

• Karlsays:

Use the first calculator. However, I see that the page is not loading exactly right. I’ll try to fix it this weekend. The calculator is only going to allow you to put in 90 cents and not 93 cents, which may lead to a penny error in the result.

• Thomassays:

How do you find something percent off some thing dollars is there a way you can do it on paper? Or like a formula to find out?

• Karlsays:

Are you asking which calculator to use? Or what’s the formula? One thing I do not discuss are the formulas. However, there are plenty of math websites. I would do a search for "percent calculations".

For solving a question with \$200 an additional 30%, how would the original cost be \$950?

• Karlsays:

Adding a percentage to a value is called a mark-up it is not covered on this page. Rather, please use this Mark-up / Discount calculator. Sorry for the confusion.

• Johnsays:

Hi Karl,
I’m having a hard time figuring out the formula to convert a certain time frame into another time frame. Ex. Let’s say the entire length of a famous battle took place in an 11 hour time period. What is the formula to condense that 11 hours into 3 hours? Furthermore, Let’s say at the 6th hour of the 11 hour battle, a particular thing happened that swayed the battle. What is the formula to convert that same particular thing at the 6th hour, to represent that event into a 3 hour time frame?

• Karlsays:

Hi John, sorry, but I don’t understand your questions. Are you asking me what calculator to use to find what percentage 3 hours is of 11 hours?

Also, I never discuss formulas. Basically, the comment section is provided as a why for users to ask questions about what calculator to use, or how to do a particular calculation using a calculator. It is here also for making suggestions and for, naturally, telling me how great they are. 🙂

• Mikesays:

Hi I’m not sure which calculator to use here.
if I start with \$26.50 and I end up with \$29.30 I would like to
know what is the percentage increase from the start number to the ending number.
thank you very much!

• Karlsays:

Hi, use "Percentage Calculator 4." "From this number:" 26.50 "To this number" 29.30.

Hope that helps.

• Emmasays:

Which calculator can i use to determine the percentage between two monetary amounts, say deposits and withdrawals?
e.g. spent £xxx amount but received £xxx amount back. I would like the percentage difference between the two amounts.

• Karlsays:

You can use Percentage Calculator 1. If you want to know what percent the deposit is of the withdrawal, enter deposit first. Otherwise, reverse the numbers.

• that guysays:

hi karl can you answer -16 of ? is 10

• Karlsays:

Hi. Thanks for the question. I see one reason why you had to ask it. Calculators 2, 3 and 4 were broken after an earlier update. They are now fixed.

Use calculator #2, assuming the 10 is 10%.

This Number is “X” Percent Of What Number?
This number: -16.00
is: 10.0000%
Of what number: -160.00

• Stuart P.says:

As a finance guy I use percentages frequently but they come with an unintended consequence. How do I get people to understand the relevance? Both dollars and percentages CAN be meaningful, but all numbers are not created equal.

A \$28,000 revenue deficit is far more meaningful if the department budget is \$100,000 than if it’s \$2 million. While both are the same dollar amount, they say something quite different in terms of performance.

Likewise, having a 40% decline in net profit is significantly more important if the budget is \$400,000 than if it’s \$12,000.

Is there a method to ‘score’ the two numbers (\$ & %) to demonstrate relevance?

Yeah, I know…weird question.

• Karlsays:

Hi Stuart, thanks for the comment and question.

I think the percentage is the score. Take your first point about the revenue deficit. In the first case, the deficit is 28% of the budget and in the second case, it’s 7% of the budget.

In the 2nd case, 40% is 40%. Now if you are saying that the 40% on the 12,000 is not as important to the business as 40% on \$400,000 then I would suggest that you need to use a different or additional base. If these net profits are for divisions, for example, then you could compare them with the entire company and then the percentage decline would be more meaningful because the base is the same in both cases.

Or am I missing something?

• jo shasays:

Original cost before tax ?
Amount of payment \$43,000.
What is the original cost before sales tax and what is the sales tax on the total amount of \$43,000.

• Karlsays:

I would not use the calculators on this page. Please use this markup and discount percentage calculator is idealy suited for your questions.

Fill it in this way:

```Net Amount?:                 \$0.00
Percent Increase (markup)?: 7.3800%
Percent Off (discount)?:    0.0000%
Gross Amount?:          \$43,000.00
```

The "Net Amount" will be the original amount before sales tax.

"Amount Added" is the sale tax amount.

• johnsays:

I have 529 members and from this number 64 had an emergency room visit in the past year. What is the “visit per 100” number?

Is it:
Step one (529/100) = 2.59
Step two (64/2.59) = 24.7/00

• Karlsays:

You would use "Percentage Calculator 1," if that’s your question. Once you get the percentage then you can say the visits per 100. If the percentage is 12.1% (rounded), which it is, then you can say there are 12.1 visits per 100.

• Catesays:

Hi Karl, how do I work out the percentage (discount) from \$18.1364 ex-GST if the final item price is \$3.50 ex-GST?