A percentage is a ratio written out of 100: per cent literally means “per hundred”. This calculator handles the five percentage questions people ask most often, and every answer shows the arithmetic so you can repeat it on paper or in a spreadsheet.
How to use the percentage calculator
- Choose the question you want answered from the What do you want to find? menu.
- Fill in the values that appear. Only the inputs that question needs are shown.
- Read the answer on the tape. The Show the work panel below it lists each step.
Results update as you type. Use Copy link to share a calculation with the same numbers already filled in.
Percentage formulas
Every percentage problem is a rearrangement of one relationship between a part, a whole and a rate:
From that single equation you get the three classic forms:
| Question | Formula | Example |
|---|---|---|
| What is P% of X? | (P ÷ 100) × X | 15% of 240 = 36 |
| X is what percent of Y? | (X ÷ Y) × 100 | 36 ÷ 240 × 100 = 15% |
| X is P% of what? | X ÷ (P ÷ 100) | 36 ÷ 0.15 = 240 |
Percentage change compares a new value with an old one and divides by the old value:
Worked examples
A sale discount
A jacket costs $240 and is marked 15% off. The discount is 0.15 × 240 = $36, so you pay 240 − 36 = $204. Choosing Increase or decrease X by P% with “Decrease” gives the sale price in one step.
A test score
You answered 42 of 56 questions correctly. 42 ÷ 56 = 0.75, and 0.75 × 100 = 75%.
Rent going up
Monthly rent rises from $1,450 to $1,595. The change is 1,595 − 1,450 = 145, and 145 ÷ 1,450 × 100 = 10%. That is a 10% increase.
Percentage change vs. percentage points
When the values you are comparing are already percentages — interest rates, unemployment, test pass rates — be careful with wording. A mortgage rate moving from 6% to 7% has risen by 1 percentage point, but it has increased by 16.7 percent relative to where it started. Both statements are true; they answer different questions. News reports and loan documents usually use percentage points for rate changes.
Why percentages don’t “undo” each other
Each percentage applies to whatever base it is taken from. A price raised by 20% and then cut by 20% ends up 4% lower than the original, because the cut is applied to the larger, raised price:
To reverse a percentage increase of P%, divide by (1 + P/100) instead of subtracting P%.
Quick reference: common percentages as fractions
| Percent | Decimal | Fraction |
|---|---|---|
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33⅓% | 0.333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 66⅔% | 0.666… | 2/3 |
| 75% | 0.75 | 3/4 |
Knowing a few of these makes mental math faster: 25% of anything is a quarter of it, and 12.5% is half of that.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 to turn it into a decimal, then multiply by the number. For example, 15% of 240 is 0.15 × 240 = 36.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If 48 people out of 320 said yes, 48 ÷ 320 = 0.15, so 15% said yes.
How do I find the original number from a percentage?
Divide the known part by the percentage written as a decimal. If 36 is 15% of a number, the number is 36 ÷ 0.15 = 240.
Is a 50% increase followed by a 50% decrease back to the start?
No. Increasing 100 by 50% gives 150, and decreasing 150 by 50% gives 75. Each percentage is taken of a different base, so the changes do not cancel.
What is the difference between percent and percentage points?
Percentage points measure the plain difference between two percentages, while percent change measures it relative to the starting percentage. A rate rising from 4% to 5% is up 1 percentage point, which is a 25% increase.