A percentage is simply a way of expressing a number as a fraction of 100. It is one of the most-used pieces of arithmetic in daily life — on a receipt showing a discount, a report showing sales growth, a nutrition label showing daily value, or a grade showing how many questions you answered correctly. The percentage calculator above handles the two most common percentage questions: finding a percentage of a number, and finding the percentage change between two numbers. This guide walks through the formulas behind both, with worked examples, so you can do the same calculation by hand whenever you need to.
How the percentage calculator works
Both tools on this page follow the same logic a calculator or spreadsheet uses internally. The first tool answers "what is X% of Y?" by converting the percentage to a decimal and multiplying. The second tool answers "how much did a value change, in percentage terms?" by comparing the difference to the original value. Neither calculation requires anything beyond basic multiplication and division — the tools simply remove the chance of a manual arithmetic slip and show the formula alongside the answer.
Formula: percentage of a number
To find 15% of 240, divide 15 by 100 to get 0.15, then multiply by 240. That gives 36. This is the exact calculation the first tool performs when you enter a percentage and a base number.
Formula: what percent one number is of another
If you scored 36 out of 240 on a task, divide 36 by 240 to get 0.15, then multiply by 100 to express it as a percentage: 15%. This is the inverse of the formula above, and it is useful whenever you know two raw numbers and want the relationship between them expressed as a percentage.
Formula: percentage increase or decrease
This formula always divides by the original value, not the new one. If a value rises from 50 to 65, the change is (65 − 50) ÷ 50 × 100 = 30%. If it falls from 65 back to 50, the change is (50 − 65) ÷ 65 × 100 = −23.08%. Notice that the increase and the decrease are not mirror images of each other — this is one of the most common sources of confusion with percentages, covered in more detail below.
Worked examples
| Question | Calculation | Answer |
|---|---|---|
| What is 20% of 150? | (20 ÷ 100) × 150 | 30 |
| What is 8.5% of 3,200? | (8.5 ÷ 100) × 3,200 | 272 |
| 45 is what percent of 180? | (45 ÷ 180) × 100 | 25% |
| A price rises from 80 to 92 | ((92 − 80) ÷ 80) × 100 | +15% |
| A price falls from 92 to 80 | ((80 − 92) ÷ 92) × 100 | −13.04% |
Step-by-step guide: calculating a percentage by hand
- Identify the two known numbers. Decide whether you're looking for a percentage of a number, or the percentage relationship between two numbers.
- Convert any percentage to a decimal. Divide it by 100. For example, 7% becomes 0.07.
- Multiply or divide as needed. To find a percentage of a number, multiply. To find what percentage one number is of another, divide the part by the whole.
- Convert back to a percentage if needed. If your answer is a decimal and you want it expressed as a percentage, multiply by 100 and add the % sign.
- Sanity-check the result. A quick estimate — for example, 15% is roughly a seventh, or a bit more than a tenth — helps catch typos before they become mistakes.
Real-life use cases
- Shopping: Working out the price after a storewide discount, or comparing two different percentage-off deals.
- Personal finance: Understanding how much of your income goes to a particular expense category, or how a bill compares to last month's.
- Business reporting: Expressing revenue growth, market share, or conversion rates as percentages for a clear, comparable metric.
- Cooking and scaling recipes: Adjusting ingredient quantities by a percentage when scaling a recipe up or down.
- Academic grading: Converting a raw score out of a total into a percentage grade.
- Health tracking: Understanding percentage-based recommendations, such as daily nutrient values on a food label.
Common mistakes to avoid
- Confusing percentage points with percentage change. If a tax rate moves from 5% to 8%, that is a 3 percentage point increase, but a 60% relative increase — both descriptions are correct, but they answer different questions.
- Using the wrong base for a percentage decrease. Percentage change is always calculated against the starting value, not the ending value. Reversing this gives a different, incorrect answer.
- Assuming a 50% decrease and a 50% increase cancel out. They don't, because each percentage is applied to a different base number. A value that drops 50% and then rises 50% ends up 25% lower than where it started.
- Rounding too early. Rounding an intermediate decimal before completing the calculation can introduce small errors, especially with multi-step problems.
Tips for working with percentages quickly
- To estimate 10% of any number, move the decimal point one place to the left. 10% of 240 is 24.
- To estimate 5%, halve the 10% figure. 5% of 240 is 12.
- To estimate 15%, add the 10% and 5% figures together: 24 + 12 = 36 — matching the exact answer from the example above.
- For percentage increases in everyday numbers, multiplying by (1 + percentage as a decimal) is often faster than calculating the increase separately and adding it back.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply it by the number. For example, 15% of 240 is (15/100) × 240 = 36.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For example, 36 out of 240 is (36/240) × 100 = 15%.
What is the difference between percentage change and percentage points?
Percentage change measures relative change between two values, such as a price rising from 50 to 60 being a 20% increase. Percentage points measure the raw difference between two percentages, such as an interest rate moving from 5% to 7% being a 2 percentage point increase, not a 40% increase.
Why do percentage increase and percentage decrease use different bases?
Percentage change is always calculated against the original (starting) value, not the new value. That is why decreasing a number by 50% and then increasing the result by 50% does not return you to the original number.
References
- Khan Academy — Free lessons on percentages and ratios