In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratios, fractions, and decimals. Percentages are often denoted by the symbol "%" written after the number. They can also be denoted by writing "percent" or "pct" after the number. For example, 35% is equivalent to the decimal 0.35, or the fraction 35/100.
Percentages are computed by multiplying the value of a ratio by 100. For example, if 25 out of 50 students in a classroom are male, the value of the ratio is 0.5, and multiplying this by 100 yields:
In other words, the ratio of 25 males to students in the classroom is equivalent to 50% of students being male.
Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values:
P is the percentage, V1 is the first value that the percentage will modify, and V2 is the result of the percentage operating on V1.
Example: P × 30 = 1.5 → P = 1.5/30 = 0.05 × 100 = 5%
The percentage difference between two values is calculated by dividing the absolute value of the difference between two numbers by the average of those two numbers. Multiplying the result by 100 will yield the solution in percent.
Example: |10 - 6| / ((10 + 6)/2) = 4/8 = 0.5 = 50%
Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value.
The percentage increase calculator above computes an increase or decrease of a specific percentage of the input number. It converts a percent into its decimal equivalent, and either subtracts (decrease) or adds (increase) the decimal equivalent from and to 1.
Example - 500 increased by 10%: 500 × (1 + 0.1) = 550
Example - 500 decreased by 10%: 500 × (1 - 0.1) = 450
Find % of a Number
(Percentage / 100) × Number = Result
Find What %
(Part / Whole) × 100 = Percentage
% Change
((New - Old) / Old) × 100 = % Change
So you need to figure out a percentage. Maybe it's a sale price, a tip at a restaurant, or a grade on a test. Whatever it is, our percentage calculator makes it super easy. Just plug in your numbers and boom - you get your answer.
But here's the thing. Understanding how percentages work is way more useful than just getting the answer. Once you get it, you'll be able to do quick calculations in your head. No calculator needed. Sounds cool, right?
Let's break it all down. No complicated math jargon. Just simple stuff you can actually use.
A percentage is just a fancy way of saying "out of 100." The word "percent" comes from Latin - "per centum" means "by the hundred." So when you say 50%, you're really saying 50 out of 100. Or half.
Think of it like a pizza cut into 100 slices. If you eat 25 slices, you've eaten 25% of the pizza. Simple, right?
The % sign actually evolved from a medieval symbol. Back in the 1400s, Italian merchants used "pc" to mean "per cento" (per hundred). Over time, the "p" got squished and the "c" became a circle. Pretty wild how we still use it today.
Our calculator handles three main types of percentage problems. Here's how each one works.
This is the most common one. You want to know what 15% of 200 is. Or 20% of 50. Here's what you do:
Let's say you're shopping and there's a 30% off sale on a $80 jacket. How much do you save?
Just put 30 in the "percentage" box and 80 in the "number" box. The calculator tells you: you save $24. The jacket costs $56 after the discount.
Not bad for a jacket, right?
This one's useful for grades. Say you got 42 out of 50 on a test. What percentage is that?
Put 42 in the first box and 50 in the second. The calculator shows 84%. That's a solid B or maybe even an A, depending on your teacher's scale.
Here's a quick trick: if you want to do this in your head, just divide 42 by 50. You get 0.84. Then multiply by 100. That's 84%. See? Not so hard.
This one trips people up. But it's actually pretty straightforward.
Imagine you know that 25% of your savings is $500. How much do you have total?
Put 25 in the percentage box and 500 in the "is" box. The calculator tells you: your total savings are $2,000.
Why does this work? Because 25% is one quarter. And $500 times 4 equals $2,000. Makes sense now?
Life changes. Prices go up. Salaries go up (hopefully). And sometimes things get cheaper. Our calculator handles all that.
Your rent went from $1,000 to $1,200. That's a $200 increase. But what percentage is that?
Here's the formula: (new number - old number) ÷ old number × 100
So: ($1,200 - $1,000) ÷ $1,000 × 100 = 20%
Your rent went up 20%. Ouch. But at least now you know exactly how much.
Same idea, but the number goes down. Your electric bill dropped from $150 to $120. Good news!
Formula: (old number - new number) ÷ old number × 100
So: ($150 - $120) ÷ $150 × 100 = 20%
Your bill decreased by 20%. Nice work on turning off those lights.
Percentages aren't just for math class. You use them all the time without even realizing it.
That "40% off" sign is trying to trick you. But now you're smarter. A $60 shirt at 40% off means you save $24. You pay $36. Is it worth it? Only you can decide.
Pro tip: for quick mental math, 10% is easy. Just move the decimal point. 10% of $60 is $6. Then multiply by 4 for 40%. That's $24 off. Done in seconds.
Standard tip is 15% to 20%. Here's a trick: calculate 10% first, then add half of that for 15%, or double it for 20%.
Your bill is $45. 10% is $4.50. Half of that is $2.25. So 15% is $4.50 + $2.25 = $6.75. For 20%, just double the 10%: $4.50 × 2 = $9.00.
Your server will appreciate it.
Got 18 out of 20 on a quiz? That's 90%. Divide 18 by 20, get 0.9, multiply by 100. Easy A.
What about 135 out of 150? Same thing. 135 ÷ 150 = 0.9. That's 90% again. You're consistent.
Your savings account earns 2% interest. You have $1,000 in there. After a year, you'll have $1,020. That $20 is your interest.
Not gonna make you rich. But it's better than nothing.
Everyone makes these. Even math teachers sometimes. Here's what to watch out for.
This is huge. If your interest rate goes from 5% to 7%, that's a 2 percentage point increase. But it's a 40% increase in the rate itself.
See the difference? Always check what someone means when they say "increased by 2%."
Yes, percentages can go above 100. If you have 200% of something, you have twice as much. 300% is three times.
So 200% of 5 is 10. Simple multiplication: 5 × 2 = 10.
If something goes up 10% and then another 10%, it's not up 20%. It's up 21%.
Why? Because the second 10% is calculated on the new, higher number. This is called compound percentage. It's how credit card interest works. And it's why debt can grow so fast.
Sometimes you need to find a percentage of a percentage. Like, what's 50% of 20%?
First, convert 20% to a decimal: 0.20. Then multiply by 50% (0.50): 0.20 × 0.50 = 0.10. That's 10%.
So 50% of 20% is 10%. Weird, but true.
Want to impress your friends? Here are some shortcuts.
10% of anything: Move the decimal one spot left. 10% of 250 is 25. 10% of 37 is 3.7.
5% of anything: Find 10% and cut it in half. 5% of 200 is 10 (because 10% is 20, half is 10).
1% of anything: Move the decimal two spots left. 1% of 500 is 5. 1% of 33 is 0.33.
50% of anything: Just cut it in half. 50% of 80 is 40. 50% of 17 is 8.5.
25% of anything: Cut it in half twice. 25% of 60: half is 30, half again is 15. Done.
Ever seen a survey where percentages add up to 101%? That's because of rounding. Each number was rounded to the nearest whole percent, and sometimes the total goes over or under 100%.
It's not a mistake. It's just math being messy.
If you're doing your own calculations and things don't add up, check your rounding. And remember: 99.9% of the time, the calculator is right.
Percentages are everywhere. Sales, taxes, tips, grades, interest rates, statistics. If you understand them, you make better decisions. You save money. You get better grades. You don't get tricked by "50% off" signs that actually mean nothing.
Plus, it feels good to know stuff. Like when you're at a restaurant and your friend asks "how much should we tip?" and you just know. That's a superpower.
So go ahead. Use our calculator. Play with the numbers. Try different scenarios. The more you practice, the easier it gets. And soon, you won't even need the calculator for the simple stuff.
But it's always here if you do.
Multiply the number by the percentage (as a decimal). For 20% of 50, convert 20% to 0.20, then multiply: 0.20 × 50 = 10. Or just use our calculator and let it do the work.
Percentage increase is relative to the original number. Percentage points are the absolute difference. If a rate goes from 5% to 7%, that's a 2 percentage point increase but a 40% increase. They're not the same thing.
Divide the first number by the second, then multiply by 100. For example, 30 is what percent of 50? 30 ÷ 50 = 0.6, then 0.6 × 100 = 60%. So 30 is 60% of 50.
Your calculator is showing the decimal form. 20% as a decimal is 0.20. To convert back to a percentage, multiply by 100. So 0.20 × 100 = 20%. Most calculators need you to do this step manually.
Subtract the old number from the new number, divide by the old number, then multiply by 100. If something went from 50 to 75, the increase is (75-50) ÷ 50 × 100 = 50%.
Yes. 200% means twice as much. 300% means three times. If you have 150% of something, you have 1.5 times the original amount. It's just multiplication.
Divide the discount amount by the original price, then multiply by 100. If a $80 item is on sale for $60, the discount is $20. $20 ÷ $80 × 100 = 25% off.
Percentage error = (|approximate value - exact value| ÷ exact value) × 100. It tells you how far off your guess or measurement is from the true value.
Divide the points you earned by the total points possible, then multiply by 100. If you got 85 out of 100, that's 85 ÷ 100 × 100 = 85%. That's usually a B.
This usually happens because of rounding. Each number was rounded to the nearest whole percent, and the rounding errors add up. It's normal and not a mistake in your calculation.
This is called a reverse percentage. If a number increased by 20% to become 120, divide 120 by 1.20 (which is 1 + 0.20). The original number is 100. Our calculator can do this for you.
Find 10% by moving the decimal one spot left, then adjust. For 15%, add half of the 10% amount. For 20%, double the 10% amount. On a $45 bill, 10% is $4.50, so 15% is $6.75 and 20% is $9.00.