How to Calculate a Percentage (3 Simple Ways)
By Shihab Mia June 20, 2026 5 min read
Quick answer
To find a percent of a number, divide the percent by 100 and multiply by the number. So 20 percent of 80 is 0.20 times 80, which equals 16. To find what percent one number is of another, divide the part by the whole and multiply by 100. To find percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100.
A percentage is just a fraction out of 100. The word comes from the Latin for "per hundred", so 25 percent means 25 out of every 100, or 0.25 as a decimal. Almost every real percentage question is one of three types, and once you can spot which type you are looking at, the maths is quick and always follows the same pattern.
This guide walks through all three types with worked examples, a reference table, and the mistakes that trip most people up. If you would rather skip the arithmetic, the percentage calculator does every version below and shows the working as you type.
What are the three types of percentage problems?
Nearly every percentage question falls into one of three shapes: finding a percent of a known number, finding what percent one number is of another, or finding how much something changed in percentage terms. Identify the shape first and the formula picks itself.
The three percentage question types at a glance
| Question type | What you know | What you want | Formula |
|---|---|---|---|
| Percent of a number | The percent and the whole | The part | (percent / 100) times number |
| What percent is x of y | The part and the whole | The percent | (part / whole) times 100 |
| Percentage change | An old value and a new value | The percent change | ((new - old) / old) times 100 |
How do you find a percentage of a number?
Turn the percent into a decimal and multiply it by the number. This is the most common type: a shop takes 20 percent off, or you tip 15 percent on a bill.
Formula
Result = (percent divided by 100) times the number. Example: 20 percent of 80 is 0.20 times 80, which is 16.
- Divide the percent by 100 to get a decimal. 20 becomes 0.20.
- Multiply that decimal by the number. 0.20 times 80 equals 16.
- For a discount, subtract from the original: 80 minus 16 leaves 64.
- For an increase, add it back: 80 plus 16 gives 96, or multiply by 1.20 in one step.
A quick mental trick: 10 percent of any number is that number with the decimal point moved one place left, so 10 percent of 80 is 8. From there, 20 percent is double that, 5 percent is half, and you can build most everyday percentages without a calculator.
How do you find what percent one number is of another?
Divide the part by the whole, then multiply by 100. Use this when you have two numbers and want the percentage between them, for example you scored 18 out of 24 on a test.
Formula
Percent = (part divided by whole) times 100. Example: 18 out of 24 is (18 divided by 24) times 100, which is 75 percent.
The order matters: the number you are measuring goes on top, and the total goes on the bottom. If you ever get a result above 100 percent for a part of a whole, you have almost certainly flipped the fraction.
How do you calculate percentage change?
Find the difference between the two values, divide by the original value, then multiply by 100. Use this when something goes up or down and you want the change as a percent, like a price rising from 50 to 60.
Formula
Change = ((new value minus old value) divided by old value) times 100. From 50 to 60 that is (10 divided by 50) times 100, a 20 percent increase.
A positive answer is an increase and a negative answer is a decrease. The key detail people miss: always divide by the original value, not the new one. For a deeper walk-through of this specific case, see how to calculate percentage increase.
A worked example: a discounted price with tax
Real problems often chain two steps together. Suppose a 120 dollar jacket is 25 percent off, and then 8 percent sales tax is added to the reduced price. Here is the full calculation.
- Find the discount: 25 divided by 100 is 0.25, and 0.25 times 120 equals 30.
- Subtract it from the original price: 120 minus 30 leaves a sale price of 90.
- Find the tax on the sale price: 8 divided by 100 is 0.08, and 0.08 times 90 equals 7.20.
- Add the tax to the sale price: 90 plus 7.20 gives a final price of 97.20.
Notice the tax is applied to the reduced price, not the original. Applying each percentage to the correct base at each step is the single most important habit in multi-step percentage maths.
Quick reference table
Common percentages of 200
| Percent | As a decimal | Percent of 200 |
|---|---|---|
| 5% | 0.05 | 10 |
| 10% | 0.10 | 20 |
| 15% | 0.15 | 30 |
| 25% | 0.25 | 50 |
| 50% | 0.50 | 100 |
Common mistakes to avoid
- Dividing by the new value instead of the original when finding percentage change. The denominator is always the starting number.
- Confusing percentage points with percent. A rate rising from 4 percent to 6 percent is a rise of 2 percentage points, but a 50 percent increase.
- Assuming a percentage increase and the same percentage decrease cancel out. A 50 percent rise then a 50 percent fall does not return you to the start: 100 goes to 150, then down to 75.
- Flipping the part and the whole. The smaller number goes on top when you want what percent one is of the other.
- Forgetting to convert the percent to a decimal before multiplying, which multiplies your answer by 100.
These slips are so common that reversible percentage errors show up in everyday reporting. According to the U.S. Bureau of Labor Statistics, the distinction between a percent change and a percentage-point change is one of the most frequently misstated figures in economic coverage (BLS handbook).
Do it instantly
Once you understand the method, a calculator saves time and avoids slips. The tool below handles all three question types and shows the working as you type.
๏ผ Try the free tool Percentage Calculator Free percentage calculator: find what percent of a number, percentage increase or decrease, percent change, percentage difference and reverse percentages fast.For shopping maths specifically, the discount calculator and tip calculator apply the first method for you and give the final amount directly.
Frequently asked questions
What is the basic percentage formula?
To find a percent of a number, multiply the number by the percent divided by 100. To find what percent one number is of another, divide the part by the whole and multiply by 100.
How do I add a percentage to a number?
Find the percentage of the number, then add it on. To add 20 percent to 80, work out 0.20 times 80 which is 16, then 80 plus 16 gives 96. A shortcut is to multiply by 1.20.
How do I calculate percentage change?
Subtract the old value from the new value, divide that difference by the old value, and multiply by 100. A positive result is an increase and a negative result is a decrease.
How do I turn a percentage into a decimal?
Divide the percentage by 100, which is the same as moving the decimal point two places to the left. So 45 percent becomes 0.45 and 7 percent becomes 0.07.
What is the difference between percent and percentage points?
Percentage points measure the raw gap between two percentages, while percent measures the relative change. Going from 20 percent to 25 percent is a rise of 5 percentage points, but a 25 percent increase.
How do I calculate a percentage in reverse to find the original number?
Divide the known part by its percentage in decimal form. If 16 is 20 percent of a number, divide 16 by 0.20 to get 80, the original whole.
Why can a percentage be more than 100?
A percentage above 100 means the part is larger than the whole you compared it to, which is normal for growth. Revenue doubling from 50 to 100 is a 100 percent increase, and tripling is a 200 percent increase.