Percentage Calculator
Six percentage calculators on one page: percent of a number, what percent one number is of another, percentage change, adding or subtracting a percentage, reverse percentages and percentage difference. Every answer shows the working.
Work out any percentage.
How to use Percentage Calculator
- Find the section that matches your question: percent of a number, what percent, percentage change, add or subtract a percentage, X is P% of what, or percentage difference
- Type your two numbers into that section (for add or subtract, choose Increase or Decrease)
- Read the answer and the working line under it; both update as you type
About Percentage Calculator
This percentage calculator answers the six questions people ask most often about percentages, each in its own section: what P% of a number is; what percent one number is of another; the percentage change, up or down, from one value to another; a number increased or decreased by a percentage; which number X is P% of, such as a price before tax; and the percentage difference between two numbers. Results update as you type, and a working line under each answer fills the formula in with your own numbers, so you can check the result or do it by hand next time.
The formulas are short. P% of X = P ÷ 100 × X, so 15% of 200 = 0.15 × 200 = 30. X as a percent of Y = X ÷ Y × 100, so 30 out of 120 is 25%. Percentage change = (new − old) ÷ |old| × 100; the vertical bars mean the old value is taken without its minus sign, so a plus sign always means the value went up. X increased by P% = X × (1 + P ÷ 100), and X decreased by P% = X × (1 − P ÷ 100). If X is P% of some number, that number is X ÷ (P ÷ 100). Percentage difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100.
Percentage change and percentage difference are easy to mix up. Change has a direction: it runs from an old value to a new one and divides by the old value. Difference has no before and after: it compares two numbers on equal terms and divides the gap by their average, so swapping the numbers gives the same answer. Going from 80 to 100 is a 25% increase, but the percentage difference between 80 and 100 is 20 ÷ 90 × 100 = 22.22%. Use change for prices, scores and anything tracked over time, and difference for comparing two separate measurements.
Three traps catch people out. First, going up and down by the same percentage doesn't cancel: 100 increased by 25% is 125, and 125 decreased by 25% is 93.75, because the second 25% is taken from a bigger number. Second, percent and percentage points are not the same thing: a rate that moves from 10% to 12% has gone up 2 percentage points, which is a 20% increase. Third, removing a percentage that was already added means dividing, not subtracting: 120 with 20% added on came from 120 ÷ 1.2 = 100, whereas taking 20% off 120 gives 96.
When you enter a number in the first section, a quick table shows 1%, 5%, 10% and other common percentages of it up to 100%, along with the number plus and minus each one. Below the calculators is a chart of common percentages as decimals and fractions. Results are rounded to at most 4 decimal places, and a number between −0.1 and 0.1 is given to 4 significant figures. The calculations run in your browser and the numbers you type aren't sent to a server.
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. 5% of 250 is 0.05 × 250 = 12.5, and 20% of 70 is 0.2 × 70 = 14. The first section of the calculator does this and shows the working.
- How do I calculate a percentage on a calculator?
- Turn the percentage into a decimal and multiply. For 18% of 250, type 250 × 0.18 = 45. Many basic calculators also have a % key, so 250 × 18 % may give the same answer, but what that key does varies from model to model, so the decimal method is the reliable one.
- How do I find what percent one number is of another?
- Divide the part by the whole and multiply by 100. If you got 43 questions right out of 50, that is 43 ÷ 50 × 100 = 86%. This is also how percent correct, or accuracy, on a test is worked out. Use the X is what percent of Y section.
- How do you calculate a percentage increase or decrease?
- Subtract the old value from the new one, divide by the old value and multiply by 100: (new − old) ÷ old × 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%, and going from 120 to 90 is (90 − 120) ÷ 120 × 100 = −25%. A negative answer means a decrease. If the old value is negative, this calculator divides by it without its minus sign, (new − old) ÷ |old| × 100, so a positive answer still means the value went up.
- How do I add or subtract a percentage from a number?
- Multiply by (1 + P ÷ 100) to add a percentage, or by (1 − P ÷ 100) to subtract one. 250 plus 10% is 250 × 1.1 = 275, and a 20% decrease on 70 is 70 × 0.8 = 56. The Add or subtract a percentage section does this in one step.
- How do I find the original number before a percentage was added?
- Divide by 1 plus the percentage as a decimal. A $54 total that includes 8% tax came from 54 ÷ 1.08 = $50. Taking 8% off $54 gives $49.68, which is wrong, because the 8% was worked out on $50, not on $54. In the calculator, use the X is P% of what number section with 54 and 108%.
- What is the difference between percentage change and percentage difference?
- Percentage change runs from an old value to a new one, has a direction (up or down) and divides by the old value. Percentage difference compares two values with no before and after, so it divides the gap by the average of the two and is never negative. 80 to 100 is a 25% change, but the percentage difference between 80 and 100 is 20 ÷ 90 × 100 = 22.22%.
- How do you calculate percentage error?
- Take the difference between the measured value and the true (accepted) value, ignore its sign, divide by the true value and multiply by 100: |measured − true| ÷ |true| × 100. Measuring 9.5 when the true value is 10 gives 0.5 ÷ 10 × 100 = 5% error. You can use the Percentage change section with the true value as the starting value and the measured value as the ending value, then ignore the sign.
- How do I convert a percentage to a decimal or fraction?
- Divide by 100. 25% is 25 ÷ 100 = 0.25 as a decimal, and 25/100 as a fraction, which simplifies to 1/4. To go back, multiply the decimal by 100. The table at the bottom of the calculator lists common percentages as decimals and fractions.
- What is the difference between percent and percentage points?
- Percentage points are the plain gap between two percentages, while percent describes the relative change. If a rate goes from 10% to 12%, it has risen by 2 percentage points, which is a 20% increase (2 ÷ 10 × 100).
- Why doesn't a 25% increase followed by a 25% decrease get back to the start?
- Because each percentage is taken from a different number. 100 increased by 25% is 125, but 25% of 125 is 31.25, so the decrease takes you down to 93.75, not 100. To undo a 25% increase you need a 20% decrease, because 125 × 0.8 = 100.
- What is the difference between a percentage and a percentile?
- A percentage is a part out of 100, such as getting 45 of 50 questions right (90%). A percentile is a rank within a group: scoring in the 90th percentile means you scored at or above about 90% of the people in the group, not that you got 90% of the answers right.
- Are the numbers I type sent anywhere?
- No. The calculations run in your browser, and the numbers you type are not sent to a server.