Percentage Calculator
Three calculators in one: what is X% of Y, X is what percent of Y, and the percent change from one value to another. Each answer comes with the formula filled in, so you can check the working or copy it into your homework. Free, no sign-up.
What is X% of Y?
15% of 80 = 12
(15 ÷ 100) × 80 = 0.15 × 80 = 12
X is what percent of Y?
30 is 25% of 120
(30 ÷ 120) × 100 = 0.25 × 100 = 25%
Percent change from X to Y
30% increase
((65 − 50) ÷ |50|) × 100 = (15 ÷ 50) × 100 = 30%
How to Use the Percentage Calculator
- 1. Choose the question that matches yours. What is X% of Y? finds a part. X is what percent of Y? finds a rate. Percent change from X to Y compares a starting and an ending value.
- 2. Enter the two numbers. All three calculators are always on screen and start with example values. Decimals and negative numbers are accepted.
- 3. Read the headline and the working. The big line is the answer; the line beneath shows the formula with your numbers in it.
- 4. Mind the rounding. Results are rounded to four decimal places for display.
The Three Formulas
| Question | Formula | Example from the tool |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 15% of 80 = 0.15 × 80 = 12 |
| X is what percent of Y? | (X ÷ Y) × 100 | 30 is (30 ÷ 120) × 100 = 25% of 120 |
| Percent change from X to Y | ((Y − X) ÷ |X|) × 100 | 50 to 65 is (15 ÷ 50) × 100 = 30% increase |
Percent change is always measured against the starting value, which is why it is not symmetrical. Going from 50 to 65 is a 30% increase, but going back from 65 to 50 is a 23.0769% decrease, because the same 15-point drop is now divided by 65. For the same reason, adding 25% and then taking away 25% does not get you back: 80 becomes 100, and 100 less 25% is 75. The calculator divides by the absolute value of the start, so a move from −50 to −25 reads as a 50% increase.
Worked Examples
| Situation | How to do it | Result |
|---|---|---|
| 15% off a price of 80 | Find 15% of 80, then subtract it | 12 off, so 68 |
| Add 15% sales tax to 80 | Find 15% of 80, then add it | 92 |
| Score of 45 out of 60 | 45 is what percent of 60 | 75% |
| Tip of 7.5% on a 240 bill | 7.5% of 240 | 18 |
| Price rises from 80 to 120 | Percent change from 80 to 120 | 50% increase |
| Price falls from 120 to 80 | Percent change from 120 to 80 | 33.3333% decrease |
Finding the original price
If an item costs 68 after a 15% discount, the original price is 68 ÷ 0.85 = 80, not 68 plus 15% (which would be 78.2). Divide by what is left after the percentage, not multiply by what was taken. The calculator has no separate box for this; use the formula, or check the answer with What is X% of Y?
Percent, Percentage Points and Writing Percentages
A rate that moves from 12% to 15% has risen by 3 percentage points, but by 25 percent in relative terms ((15 − 12) ÷ 12 × 100). Say which you mean, particularly in research writing. For the symbol, APA uses the % sign with numerals (25%), while Chicago spells out percent in running text outside scientific and technical writing (25 percent). Follow the style your instructor or journal requires.
Which Tool Do You Need?
| You want to… | Use |
|---|---|
| Find a percent of a number, a rate, or a percent change between two values | This calculator |
| Compare a measured value with an accepted one | Percent Error Calculator |
| Work out where a score sits among others | Percentile Calculator |
| Convert markup to margin | Markup and Margin Calculator |
| Turn a decimal into a fraction | Decimal to Fraction Converter |
Frequently Asked Questions
- How do I calculate a percentage of a number?
- Divide the percentage by 100 and multiply by the number: 15% of 80 is 0.15 × 80 = 12. In the tool, use What is X% of Y?, enter 15 and 80, and the working is shown beneath the answer.
- How do I find what percent one number is of another?
- Divide the part by the whole and multiply by 100. 30 out of 120 is (30 ÷ 120) × 100 = 25%. Use X is what percent of Y? with the part as X and the whole as Y; the whole cannot be zero.
- How do I calculate percent increase or decrease?
- Subtract the starting value from the ending value, divide by the starting value, and multiply by 100. A positive answer is an increase and a negative one a decrease. The tool labels the answer for you, so 50 to 65 reads as a 30% increase.
- Why isn't a 25% rise followed by a 25% fall back where I started?
- Each percentage applies to a different base. 80 plus 25% is 100, but 25% of 100 is 25, which takes you to 75. To get back from 100 to 80 you need a 20% fall.
- What is the difference between percent and percentage points?
- Percentage points are the simple difference between two percentages; percent change is relative to the first one. Moving from 12% to 15% is 3 percentage points, or a 25% increase.
- Why won't the calculator accept zero?
- Dividing by zero has no answer. The whole in X is what percent of Y, and the starting value in a percent change, must be non-zero. If your start is zero, the change is undefined as a percentage; report the absolute change instead.