Percentage Calculator
Work out X% of Y, what percent X is of Y, percent increase or decrease, and percentage difference, each with the formula and steps shown.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Percentage Calculator?
Most percent questions are one of a handful of sentences: what is 20% of 150, 30 is what percent of 150, 30 is 20% of what, how much did a price change from 80 to 100, and how far apart are two readings. This page lays all of them out as plain sentences with two boxes each, so you never have to decide which formula you need. Type into the sentence that matches your question and the answer appears underneath.
Every row has a "Formula and steps" panel that shows the arithmetic with your numbers, which is handy for homework, for checking a spreadsheet, or for explaining a figure to someone else. Results are cleaned of floating-point noise, so 7% of 0.3 shows as 0.021 rather than 0.021000000000000001.
Nothing is sent anywhere: the maths runs in your browser, and the share link stores your inputs in the page address so a colleague sees the same numbers.
- Seven percent questions on one page, each written as a sentence
- Formula and step-by-step working for every answer
- Percent change and percentage difference side by side, with a note on which to use
- Clean decimals without floating-point artefacts
- Copy all results and share inputs with a link
How to use the Percentage Calculator
- Find the sentence that matches your question, for example "What is _% of _?" for a tip or a tax amount.
- Type the two numbers into its boxes. Decimals and negative numbers are accepted, and commas are ignored.
- Read the answer under the sentence. Percent change shows a plus sign for an increase and a minus for a decrease.
- Open "Formula and steps" to see the calculation written out with your values.
- Use Copy result to copy every answer on the page, or Share link to send the inputs to someone else.
Worked examples
Percent of a number
Input
What is 20% of 150?
Output
30
20% is 0.2, and 0.2 × 150 = 30. Swapping the numbers gives the same result: 150% of 20 is also 30.
A rise and the fall back
Input
From 80 to 100, then from 100 to 80
Output
+25% and −20%
The change of 20 is divided by 80 the first time and by 100 the second, which is why equal-sized moves give different percentages.
Two lab readings
Input
Difference between 10 and 15
Output
40%
The gap of 5 is divided by the average 12.5. Percent change would say 50% (from 10) or 33.3% (from 15), depending on which you call the start.
Adding and removing 15%
Input
Add 15% to 80; take 15% off 80
Output
92 and 68
Multiplying by 1.15 or by 0.85 does it in one step. Taking 15% off 92 gives 78.2, not 80, for the same base-shift reason.
Background and insight
"Per cent" means per hundred, from the Latin per centum. A percentage is a ratio with 100 as its denominator, so 20% is 20/100, or 0.2. Each row on this page is the same equation, part = percent / 100 × whole, rearranged to solve for whichever of the three quantities is missing.
Percent change and percentage difference are often confused. Percent change has a direction and a reference value: (new − old) / |old| × 100. Because the base changes, a 25% rise from 80 to 100 is undone by a 20% fall, not a 25% one. Percentage difference has no reference: it divides the gap by the average of the two values, |A − B| / ((|A| + |B|) / 2) × 100, and gives the same answer whichever number comes first. Scientists use it to compare two measurements; shops and statisticians reporting growth use percent change.
Percentage points are a third idea again. An interest rate moving from 4% to 5% rose by one percentage point, which is a 25% increase in the rate. News reports mix the two, and the gap can be large.
Common use cases
Shopping and bills
Find a tip, a sales tax amount or the price after a markdown without mixing up which number is the base.
Grades and scores
Turn 42 marks out of 56 into a percentage (75%), or find how many marks 80% of a 60-mark paper needs (48).
Reports and dashboards
Calculate month-on-month change for revenue, traffic or headcount, with the correct sign and base.
Science and engineering
Compare two measurements or two methods with percentage difference when neither is the accepted value.
Tips and limitations
- Percent change from zero is undefined, because there is no base to divide by. The calculator says so instead of printing infinity.
- For a negative starting value the change is divided by its absolute value, so going from −50 to −25 reads as a 50% increase.
- Successive percentages multiply rather than add: +10% then +10% is +21%, and −50% then +50% leaves you at 75% of where you started.
- If the answer should be a count of people or items, round it yourself at the end; the calculator keeps full precision.
- To reverse a percentage (find the price before tax), use "_ is _% of what?" with 100% plus the rate, such as 108 is 108% of 100.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 20% of 150 is 0.20 × 150 = 30. In the calculator, use the first sentence, "What is _% of _?".
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 150 is 30 / 150 = 0.2, which is 20%. The whole goes on the bottom, so 150 is 500% of 30, not 20%.
What is the formula for percent increase or decrease?
Percent change = (new value − old value) / |old value| × 100. A result above zero is an increase, below zero a decrease. From 80 to 100 is (100 − 80) / 80 = +25%.
What is the difference between percent change and percentage difference?
Percent change measures movement from a starting value and depends on which number is the start. Percentage difference compares two values with no reference, dividing their gap by their average. For 10 and 15, percent change is +50% (from 10) while percentage difference is 40% either way.
How do I find the original number before a percentage was added?
Divide by 1 plus the rate. A price of 108 including 8% tax was 108 / 1.08 = 100 before tax. In the calculator, use "_ is _% of what?" with 108 and 108.
Why does a 50% drop need a 100% rise to recover?
Because each percentage uses a different base. Falling 50% from 200 leaves 100, and getting back to 200 means adding 100, which is 100% of the new, smaller value.
What is a percentage point?
It is the plain difference between two percentages. A rate going from 4% to 5% rose by 1 percentage point, which is a 25% relative increase. Use points for the gap and percent for the relative change.
Is there an in-depth guide to the Percentage Calculator?
Yes. “Percentages, Fractions and Ratios: How the Arithmetic Fits Together” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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