Percentage Calculator
Find out how much a percentage of a value is, apply a discount or an increase, compare two numbers and work back from a result to the original value, with every calculation explained.
Educational use: results are estimates made for study and reference. Checking the answer and deciding what to do with it is the sole responsibility of whoever uses the tool. Read the legal notice.
On this page
- How to use the calculator, no fuss
- Solved examples, from simple to tricky
- The formulas behind each option
- Mistakes everyone makes (and how to avoid them)
- Shortcuts for mental math
- What to expect from the result
- Seeing a percentage
- What people ask most
- Where "percent" comes from
- Where this math shows up in real life
- Words you will meet in these calculations
- Fun facts that help you remember
- Keep learning
How to use the calculator, no fuss
The form changes with the type of calculation you pick, so you only see the fields that apply. There are four steps:
- Choose the type of calculation in the first field. If you are unsure, the descriptions below will help.
- Type the numbers. Use a period as the decimal mark (12.5). You do not need to type the % symbol.
- Click Calculate. The result appears highlighted and, right below it, the step-by-step work shows how it was obtained.
- Copy or clear. The copy button sends the result to a spreadsheet or message; the clear button resets everything.
Which option should you choose?
- What is X% of a value: "what is 15% of 200?" The classic question.
- A value is what % of another: "I got 42 out of 60 questions right, what percentage is that?"
- Increase by X%: starts from a value and applies an increase, also showing the size of the increase.
- Take X% off: the reverse: the final price and how much came off the original.
- Percent change: compares a starting value with a final one and tells you whether it went up or down, and by how much.
- Find the total from a part: when you know what a slice is worth and what share it represents, and you want to find the whole.
Solved examples, from simple to tricky
1. The shop-window discount
A pair of sneakers costs $240 and is 35% off. How much do you pay?
You pay $156 and save $84.
2. The test score
You got 42 out of 60 questions right. What was your score?
A score of 70%.
3. A growing town
A town had 8,400 residents and now has 9,282. How much did it grow?
Growth of 10.5%.
4. Going back to the original price
Someone paid 180 for a product that was 20% off. What was the price before?
The original price was 225. Careful: adding 20% to 180 does not work, because the 20% was taken from the old price, not the new one (180 × 1.20 would give 216, not 225).
5. The trap of back-to-back changes
A value goes up 20% and then drops 20%. Does it return to the starting point?
No. It ends up 4% below where it started, because the 20% drop was applied to a larger value (120) than the increase was (100). This asymmetry is behind a lot of confusion in news stories and sales.
The formulas behind each option
Percentages seem to come with plenty of rules, but it all boils down to one idea: divide by 100. Saying "15%" is the same as saying "15 hundredths," or 0.15. With that, the six calculations in the calculator look like this:
Part of a value
What percent one value is of another
Percent increase
Percent discount
Percent change
Total from a part
Notice the trick for increases and discounts: instead of working out the percentage and then adding or subtracting it, you multiply once by the factor. A 20% increase becomes × 1.20. A 20% discount becomes × 0.80. It is faster and avoids mistakes.
Mistakes everyone makes (and how to avoid them)
Confusing percent with percentage points
If a rate goes from 10% to 12%, it rose by 2 percentage points, but it increased by 20% in relative terms (2 ÷ 10). Both statements are true, and hearing one while thinking of the other causes a lot of misunderstandings.
Applying the second percentage to the wrong base
A 10% increase followed by another 10% increase is not a 20% increase. It is 1.10 × 1.10 = 1.21, or 21%. The second increase applies to a value that has already grown.
Dividing by the wrong number in a percent change
Percent change always divides by the starting value. From 50 to 65 is a 30% rise (15 ÷ 50). From 65 to 50 is a 23.08% drop (15 ÷ 65). The same jump of 15 units gives different percentages depending on the starting point.
Adding discounts together
Two successive discounts of 20% and 10% do not make 30%. They make 0.80 × 0.90 = 0.72, which is a 28% discount in total.
Rounding too early
If you round the result of every step, the error grows with each one. Keep all the decimal places and round only at the end.
Forgetting what the "whole" is
"20% more" and "20% of the total" are different calculations. Before calculating, ask yourself: 20% of what?
Shortcuts for mental math
You cannot always open a calculator. Almost every everyday percentage comes from two easy calculations: 10% (move the decimal point one place to the left) and 50% (divide by two). Taking 240 as an example:
| Percentage | How to think about it | Result on 240 |
|---|---|---|
| 1% | divide by 100 | 2.4 |
| 5% | half of 10% | 12 |
| 10% | move the decimal point one place left | 24 |
| 20% | double 10% | 48 |
| 25% | a quarter (half of a half) | 60 |
| 50% | half | 120 |
| 75% | three quarters (50% + 25%) | 180 |
For increases and discounts, the multiplying factor saves steps:
| Change | Multiply by | Change | Multiply by |
|---|---|---|---|
| +5% | 1.05 | −5% | 0.95 |
| +10% | 1.10 | −10% | 0.90 |
| +20% | 1.20 | −20% | 0.80 |
| +50% | 1.50 | −50% | 0.50 |
And one more table to help you understand the asymmetry in example 5: how much does a value need to rise to make up for a drop?
| Drop | Rise needed to get back |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 50% | 100% |
What to expect from the result
The calculator rounds the display to up to six decimal places, but it does the math with the precision browsers use, which is about 15 significant digits. For the vast majority of uses, that is more than enough.
A few precautions are worth taking: if the result is a price, round it to two decimal places in whatever way your situation calls for (every store and every system rounds differently); if you are studying, check the step-by-step work and redo the problem once with the rule of three. This tool does not account for taxes, interest, fees or specific business rules, only the math of percentages.
Bottom line: this tool is educational. Results do not replace your own checking, and how you use them is entirely your responsibility. More details in the legal notice.
Seeing a percentage
A full bar is worth 100%. Any percentage is just a piece of that bar, and the rest is what is left over. This drawing shows 35% of a total:
What people ask most
How do I calculate a percentage in my head?
Start from 10% (move the decimal point one place to the left) and 50% (half). From those you can build almost anything: 5% is half of 10%, 20% is double 10%, 15% is 10% plus 5%. See the shortcuts table on this page.
What is the difference between a percentage and a percentage point?
A percentage point is the simple difference between two rates. A percentage is the relative change. If a rate goes from 10% to 12%, it rose by 2 percentage points and by 20% in relative terms.
How do I calculate a 10%, 15% or 25% discount?
Multiply the price by the discount factor: 0.90 for 10%, 0.85 for 15% and 0.75 for 25%. A product priced at 80 with 15% off comes to 80 × 0.85 = 68.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If 30 is part of 120: 30 ÷ 120 = 0.25, which is 25%. In the calculator, choose the option "A value is what % of another."
Can a percentage be greater than 100%?
Yes. Going over 100% means the value exceeds the reference. If something doubled, it grew by 100%; if it tripled, it grew by 200%. What does not exist is a discount of more than 100%, which would push the price below zero.
Does a 20% increase followed by a 20% discount return to the starting value?
No. You end up 4% below. The increase applies to the original value, and the drop applies to the already increased value, which is larger. That is why 100 → 120 → 96.
How do I find the price before the discount?
Divide the amount paid by the discount factor. If you paid 180 with 20% off, the factor is 0.80 and the original price was 180 ÷ 0.80 = 225. Use the option "Find the total from a part" and enter 80%.
Why does the percent change differ if I swap the values?
Because the base of comparison changes. From 50 to 65, the rise is 30%. From 65 to 50, the drop is 23.08%. The absolute difference is the same (15), but the starting point is not.
Can I use a comma as a thousands separator?
It is best not to. Use a period as the decimal mark and write large numbers with no thousands separator (for example, 12500).
Can this calculator work out interest?
No. Interest involves time and compounding, which is a different calculation. Here the percentage is applied just once to a single value.
Where "percent" comes from
The word comes from the Latin per centum, "by the hundred." The idea of expressing parts out of a hundred is an old one: the Romans already collected taxes at fixed fractions, such as one hundredth on goods sold at auction, and used fractions with a denominator of 100 to make money and sharing calculations easier.
The % symbol is much more recent. Historians point to Italian commercial manuscripts from the 15th and 16th centuries, in which "per cento" was gradually abbreviated by hurried scribes until it became a "c" with a stroke and, later, the shape we know today. The exact path is not settled, which is what makes the story fun.
Why did 100 catch on? Because it makes comparisons fair. Saying that store A gave $30 off and store B gave $45 off tells you nothing without knowing the price of each product. Saying "10%" and "15%" puts both discounts on the same ruler.
Where this math shows up in real life
- Shopping and sales. Comparing "30% off" with "buy 3, pay for 2" means converting everything to a common base, and percentages do that job.
- School and tests. Scores on questions, the weight of each exam in a grade, and comparisons between classes.
- Reading news and surveys. "The rate rose 12%" only makes sense if you know where it started and whether it is a percentage or a percentage point.
- Recipes and scaling. Increasing a recipe by 50%, or diluting a paint to 80% concentration, is multiplying by a factor.
- Sports. Shooting percentages, share of possession, progress in personal records.
- Technology. Battery level, memory use and storage space are all shown as percentages.
- Measurements and tolerances. In workshops and labs, margins of error are often given as a percentage of the measured value.
Words you will meet in these calculations
- Percentage
- A fraction with a denominator of 100. Writing 15% is the same as writing 15/100 or 0.15.
- Total value (whole)
- The number used as the reference, the one that represents 100%.
- Partial value (part)
- The piece of the whole whose percentage you want to know.
- Multiplying factor
- The number you multiply a value by to apply an increase or discount in one go (1.20 for +20%, 0.80 for −20%).
- Percent change
- How much, in percent, a value has changed relative to its starting value.
- Percentage point
- The arithmetic difference between two percentages. From 10% to 12% is 2 percentage points.
- Base
- The value the percentage is applied to. Changing the base changes the result.
Fun facts that help you remember
- X% of Y equals Y% of X. Calculating 8% of 50 looks like work, but 50% of 8 is just half: 4. It always works, because multiplication does not care about the order of the factors.
- A percentage can go over 100%. A value that tripled grew by 200%, and saying someone "gave 110%," although an exaggeration, is mathematically possible.
- There is a "per thousand." The ‰ symbol means parts per thousand and shows up, for example, in the salinity of seawater.
- Basis point. In technical fields, 1 basis point equals 0.01%, which is useful for talking about very small changes without ambiguity.