Percentage Calculator
Work out a percentage of a number, a percentage change, a discount, a reverse percentage and more. Ten calculators in one place, with every step shown in plain words. Nothing you type leaves your phone.
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Percentages explained in plain words, with worked examples
Percentages turn up everywhere: exam results, shop signs, salary letters, fuel prices and the bill at the end of a meal. Most of us learn the idea at school and then quietly forget which number goes on top. If that sounds like you, you're in good company. This guide goes through the ideas one at a time, in simple words, with small examples. The calculator above does the sums in a blink, and everything below explains why the answers look the way they do.
What a percentage really means
“Percent” just means “out of one hundred”. If you got 85% in a test, it's the same as saying you'd get 85 marks if the paper were out of 100. The little % sign is a short way of writing “divided by 100”. So 50% is 50 out of 100, which is half, which is 0.5 as a decimal. They're three ways of writing one idea.
That's why percentages are so handy. They let us compare things of different sizes. A shop that gives 300 off a 1,500 shirt and another that gives 500 off a 5,000 pair of shoes are hard to compare in money. In percent, the first is 20% off and the second is 10% off, and now you can see which deal is better at a glance.
Here's a small table of friends you'll meet again and again. Notice how each one can be written as a fraction, a decimal and a percent. The last column says what it means in everyday talk.
| Percent | Fraction | Decimal | In everyday words |
|---|---|---|---|
| 10% | 1/10 | 0.1 | one part in ten |
| 25% | 1/4 | 0.25 | a quarter |
| 50% | 1/2 | 0.5 | half |
| 75% | 3/4 | 0.75 | three quarters |
| 100% | 1 | 1 | the whole thing |
| 12.5% | 1/8 | 0.125 | one eighth |
Percentages can go past 100, too. If your sales this month are 150% of last month's, you sold one and a half times as much. They can also be negative when we talk about change, such as −8% for a price that fell.
How to calculate X% of a number
This is the sum people do most often, and it only has two steps. First turn the percent into a decimal by dividing by 100. Then multiply that decimal by your number. That's all. The picture below shows the idea using the first example, 15% of 2,400.
Let's try it with marks. Suppose a school fund-raiser collected 2,400 and 15% of it goes to the library. Divide 15 by 100 to get 0.15, then multiply 0.15 by 2,400. The answer is 360. Another quick one: 12.5% of 800. Divide 12.5 by 100 to get 0.125, then 0.125 × 800 = 100.
There's an easy mental way too. Find 10% by moving the decimal point one place to the left, then build up from there. For 2,400, 10% is 240, and 5% is half of that, which is 120. So 15% is 240 + 120 = 360, the same answer without a calculator. We'll practise more of these in the mental-math section.
What percent one number is of another
Now the question turned around: you know the part and the whole, and you want the percent. Divide the part by the whole, then multiply by 100. The order matters. The whole always goes on the bottom.
Worked example: exam marks
You scored 68 marks in a test out of 80. What percent is that?
Step 1: 68 ÷ 80 = 0.85.
Step 2: 0.85 × 100 = 85.
So you scored 85%.
It works for anything. If 360 of the 2,400 students in a school are in Grade 6, then 360 ÷ 2,400 = 0.15, which is 15%.
A quick check: if the part is smaller than the whole, the answer must be under 100%. If it isn't, the numbers may be the wrong way round.
Percentage increase and decrease, step by step
Percentage change tells you how much something grew or shrank compared with where it started. There are three steps. Find the difference (new minus old). Divide that difference by the old number. Multiply by 100.
Worked example: a salary increment
Your salary goes from 85,000 to 93,500.
Step 1: 93,500 − 85,000 = 8,500.
Step 2: 8,500 ÷ 85,000 = 0.1.
Step 3: 0.1 × 100 = 10.
That's a 10% increase.
Falls work exactly the same way, and the answer simply comes out negative. If petrol goes from 370 to 340 a litre, the change is 340 − 370 = −30. Divide by the old price: −30 ÷ 370 = −0.0811, so the price fell by about 8.11%.
Always divide by the old number, the one you started with. That one idea fixes most percent-change mistakes. To add or subtract a percentage from a number, you can also do it in one go: for a 15% rise, multiply by 1.15, and for a 15% fall, multiply by 0.85. So 2,400 plus 15% is 2,400 × 1.15 = 2,760, and minus 15% is 2,400 × 0.85 = 2,040.
If you only want the amount that changed, stop after step 1. In the salary example that is 8,500.
Why +20% then −20% doesn’t bring you back
This surprises almost everyone. You add 20% to a number, then take 20% off the result, and you end up lower than where you began. It isn't a trick. The two 20%s are taken from different starting points.
Start with 1,000. Add 20% and you get 1,200. Now take 20% off 1,200. Twenty percent of 1,200 is 240, so you land on 960. You lost 40, which is a 4% drop overall. The second 20% was taken from a bigger number, so it removed more rupees than the first one added.
| Step | What happens | Value |
|---|---|---|
| Start | Where you begin | 1,000 |
| +20% | 1,000 × 1.20 | 1,200 |
| −20% next | 1,200 × 0.80 | 960 (not 1,000) |
| To get back from 1,200 | You need −16.67%, since 200 ÷ 1,200 | 1,000 |
| Or: −20% first, then | 1,000 × 0.80 = 800, and you need +25%, since 200 ÷ 800 | 1,000 |
The rule of thumb: a rise is undone by a smaller percent fall, and a fall needs a bigger percent rise to undo it. It's why a price that is 50% off needs a 100% rise to get back to the start.
Reverse percentages: finding the original
Sometimes you know the end result and the percent, and you need the start. For example, a phone is now 4,500 after a 25% discount. What was the original price? The tempting move is to add 25% of 4,500 back on, but that gives the wrong answer, because the 25% was taken from the original and not from 4,500.
Here's the right way. After a 25% discount you pay 75% of the original, which is a multiplier of 0.75. To undo it, divide by 0.75: 4,500 ÷ 0.75 = 6,000. The original price was 6,000. You can check: 25% of 6,000 is 1,500, and 6,000 − 1,500 = 4,500. It matches.
Worked example: before a 20% increase
After a 20% increase, a shop's monthly sales are 1,200 units. What were they before?
A 20% rise means the new number is 120% of the old one, a multiplier of 1.2.
1,200 ÷ 1.2 = 1,000.
The other kind of reverse question is “this part is P% of what?” If 360 is 15% of a number, first find 1% by dividing 360 by 15, which gives 24. Then multiply by 100 to get the whole: 2,400. The calculator's “Reverse percent” tab handles both kinds and adds a one-line note on why we divide.
Percentage difference vs percentage change
These two sound alike but answer different questions. Percentage change has a clear before and after. Percentage difference compares two numbers when neither one is the starting point, for example the prices of the same book in two shops, or the heights of two friends.
To find the percentage difference, take the gap between the two numbers and divide it by their average, then multiply by 100. For 80 and 100, the gap is 20 and the average is 90, so the difference is 20 ÷ 90 × 100 = 22.22%. The order of the two numbers doesn't matter. Change, on the other hand, does depend on the order: going from 80 to 100 is a 25% increase, and from 100 to 80 is a 20% decrease.
| Idea | Question it answers | Formula | Example |
|---|---|---|---|
| Percent change | How much did it grow or shrink from the start? | (new − old) ÷ old × 100 | 80 to 100 is +25%; 100 to 80 is −20% |
| Percentage difference | How far apart are two numbers when neither is the start? | gap ÷ average × 100 | 80 and 100 are 22.22% apart, either way round |
| Percentage points | What is the plain gap between two percentages? | new % − old % | 10% to 12% is 2 points |
Percentage points vs percent
Imagine a savings rate that moves from 10% to 12%. The plain gap is 2, and we call that 2 percentage points. But 2 is also 20% of the original 10, so you could say the rate went up by 20%. Both are true, and they mean different things.
Headlines mix them up all the time, which can make a small change sound huge. “The pass rate rose 5%” might mean it went from 60% to 63%, which is 3 points, or from 60% to 65%, which is 5 points. When it matters, look for the word “points” or the two actual percentages.
A good habit is to say which one you mean. A rate going from 8% to 9% is “up one percentage point”, or “up 12.5% in the rate itself”, since 1 ÷ 8 = 0.125. The “Points vs percent” tab shows both.
Mental-math tricks for 10%, 5%, 15%, 25% and 50%
You don't need a calculator for the percentages people use most. All of them grow out of 10%, and 10% is easy: move the decimal point one place left. Take a bill of 3,600.
3,600 in your head
Start from 10% and build every other answer from it.
All five come from one move: shift the decimal point to get 10%, then halve, double or add.
- 10%: move the decimal point left once. 3,600 becomes 360.
- 5%: half of 10%. Half of 360 is 180.
- 15%: 10% plus 5%. That's 360 + 180 = 540.
- 25%: a quarter, or half of half. Half of 3,600 is 1,800, and half again is 900.
- 50%: simply half. 1,800.
Two more tricks are worth keeping. For 1%, move the decimal point two places, so 1% of 2,400 is 24, and you can multiply that for any whole percent. And percentages are flippable: X% of Y equals Y% of X. So 8% of 50 is the same as 50% of 8, and the second one is just half of 8, which is 4. When a sum looks awkward, flip it and see whether it gets easier.
Percentages in everyday life
Once you see the pattern, you spot the same few sums all over your day. Here are the ones we get asked about most, with a quick example and a calculator that goes deeper if you need it.
Discounts. A 30% seasonal offer on a 7,500 dress saves 30% of 7,500, which is 2,250, so you pay 5,250. For stacked offers, coupons and original prices, try our Discount Calculator.
Tips and shared bills. A 10% tip on a 4,800 meal is 480. If six friends are splitting the bill, the Tip & Bill Split Calculator shares the tip, tax and leftover cents fairly.
Marks and grades. Add up the marks you got and the marks available, then divide. Two subjects marked out of different totals can give a different answer from the plain average of the percentages. Our “Marks and grades” tab shows both, and the Average Calculator is handy when you only need a mean.
Salary and prices. A raise from 85,000 to 93,500 is 10%. A fuel price drop from 370 to 340 is about 8.11%. Always compare against the old figure.
Interest and loans. A simple yearly interest of 8% on 50,000 is 4,000 a year. Real loans repay in instalments with interest on the remaining balance, so for those use the Loan EMI Calculator rather than a quick percentage.
Time and business. Counting days comes first when you want a percentage of a period, and the Age & Date Calculator does that. Small-business owners use percentages for profit: if an item costs 12,000 and sells for 15,000, the 3,000 profit is 25% of the cost (markup) but only 20% of the selling price (margin). Both are right, but they answer different questions, so say which one you mean.
Common mistakes
The most common slip is dividing by the wrong number. For percent change, divide by the old value. For “what percent is A of B”, divide by B, the whole. If your answer looks surprising, swap them and see whether it makes more sense.
The second is adding and subtracting percentages as if they were plain numbers. A 20% rise followed by a 20% fall doesn't cancel out, as we saw. In the same way, two 10% discounts, one after the other, are 19% off in total and not 20%, because the second one is taken from the already lower price.
Third, confusing percentage points with percent. Fourth, typing 15 where a spreadsheet needs 0.15, because the % sign means “divided by 100”. And last, rounding too early: three lots of 33% don't make a whole. Keep a few extra decimals in the middle of a sum and round only at the end.
When you want a second opinion, the calculators hub has more tools for everyday sums in one place.
Frequently asked questions
How do you calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 2,400, work out 15 ÷ 100 = 0.15, then 0.15 × 2,400 = 360.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you scored 68 out of 80, then 68 ÷ 80 × 100 = 85%.
How do you calculate percentage increase or decrease?
Subtract the old value from the new one, divide by the old value, then multiply by 100. Going from 80 to 100 is a 25% increase, and going from 100 to 80 is a 20% decrease.
How do I add or subtract a percentage from a number?
Work out the percentage amount and add it or take it off, or multiply once by 1.15 to add 15% and by 0.85 to subtract 15%. For 2,400, that gives 2,760 and 2,040.
Why doesn’t +20% then −20% give me back my number?
The second 20% is taken from a bigger number, so it removes more than the first one added. 1,000 becomes 1,200, then 960, which is a 4% loss overall.
How do I find the original number after a percentage change?
Divide the new value by the multiplier. After a 25% discount, the price is 75% of the original, so 4,500 ÷ 0.75 = 6,000. Don’t add 25% back onto 4,500.
What is the difference between percentage change and percentage difference?
Change compares a new value with an old starting value, so the order matters. Difference compares two values with their average, so the order doesn’t matter. For 80 and 100, the difference is 22.22%.
What is the difference between percentage points and percent?
Percentage points are the plain gap between two percentages. A rate moving from 10% to 12% is up 2 points, which is a 20% rise in the rate itself.
Can a percentage be more than 100%?
Yes. If this month’s sales are 150% of last month’s, you sold one and a half times as much. A percentage over 100 just means the part is bigger than the whole you compared it with.
Is my information saved or sent anywhere?
No. The sums happen in your browser, and nothing you type is stored or sent. A share link keeps your numbers inside the link itself, so only people you send it to can open that calculation.
Disclaimer
This calculator and guide are for learning and everyday use. They give estimates based on the numbers you type, so please check anything that matters, such as money, tax, grades or legal figures, against an official source or a qualified professional. Tax rates, discount rules and grading schemes differ by place and can change.
Method: how the numbers are worked out
Every number is held as an exact fraction, so there are no tiny floating-point errors such as 0.1 + 0.2 giving 0.30000000000000004. Rounding happens only at the very end, when the answer is shown, and it rounds half up (so 0.125 becomes 0.13). Percent change divides by the size of the starting value, and percentage difference divides by the average of the two sizes. Reverse percentages divide by the multiplier, such as 1.20 for an increase of 20%.