Percentage Calculator and Guide

What a percentage is, and how decimals and fractions compare

Percent means per hundred. Eighteen percent is 18 out of every 100, which is the fraction 18/100 and the decimal 0.18. That is the whole idea, and every problem on this page is a consequence of it.

A 10 by 10 grid makes it visible. Shade 18 of the 100 squares and you have shaded 18 percent of the grid. Shade 50 and you have half. Shade all 100 and you have 100 percent, the whole thing.

Three anchors cover most of the percentages people meet in a day: 1 percent is one hundredth, 10 percent is one tenth, and 100 percent is all of it. A pay raise of 3 percent is 3 cents on every dollar. A sales tax of 8.25 percent is 8.25 cents on every dollar.

Percentages above 100 are allowed, and they mean more than the whole. A town whose population grows 150 percent ends up with two and a half times as many people, because the original 100 percent is still there.

Three labels for one value

Every percent can be written three ways, and moving between them comes down to where the decimal point sits.

• Percent to decimal: divide by 100, so 18% = 0.18 and 7.5% = 0.075.
• Decimal to percent: multiply by 100, so 0.62 = 62% and 1.4 = 140%.
• Fraction to percent: divide the top by the bottom, then multiply by 100. For 3/8, 3 divided by 8 is 0.375, and 0.375 x 100 = 37.5 percent.

The direction of the decimal move is the step people get wrong. 0.06 is 6 percent, not 60. 0.6 is 60 percent. 6 is 600 percent. Say the decimal out loud as six hundredths and the percent follows.

Halves, quarters, fifths and eighths are worth memorizing because they cover most fractions in recipes, sales and test scores. Thirds repeat forever, so any printed percent for 1/3 is rounded.

The six questions a percent problem can ask

Word problems look different from each other, but they almost always ask one of six questions. The workbench at the top of the page runs every one of them, and the table below shows the setup for each.

The last two rows use the same division, but the story is different. In one, the part is a number you were handed and you want the starting figure it belongs to. In the other, the part is a group of people or objects and you want the size of the whole group.

The most common error across all six is comparing against the wrong starting figure. The starting figure is the number the percent is taken of, and it is not always the biggest number on the page or the one printed last.

Worked example: a test score, a price rise and a sale tag

Start with a test of 40 questions where a student gets 34 right. The score is the part over the whole: 34 divided by 40 is 0.85, so the score is 85 percent. The 6 missed questions are 15 percent, and the two figures add to 100 percent because they come from the same 40 questions.

Next, a pair of headphones goes from 40 dollars to 46 dollars. The change is 6 dollars. Divide the change by the starting price: 6 divided by 40 is 0.15, so the price rose 15 percent. Dividing 6 by 46 gives 13.04 percent and that answers a different question, what share of the new price the increase represents.

Then a jacket is tagged 72 dollars after a 25 percent markdown. The tag is 75 percent of the old price, so the old price is 72 divided by 0.75, which is 96 dollars. Adding 25 percent to 72 gives 90, and 90 is the wrong answer because the 25 percent came off the larger original price, not off the sale price.

Mental math: 10, 15 and 20 percent without a calculator

Most tips, taxes and sale signs can be handled in your head once 10 percent is automatic. Ten percent of a number is the number with the decimal moved one place left. On a bill of 36.80, 10 percent is 3.68.

From there, build the others. Five percent is half of 10 percent, so 1.84. Fifteen percent is 10 plus 5, so 5.52. Twenty percent is twice 10 percent, so 7.36. Twenty-five percent is a quarter, which means dividing by 4, so 9.20.

Eighteen percent, a common restaurant tip, is 20 percent minus 2 percent. The 20 percent is 7.36 and 2 percent is two lots of 1 percent, or 0.74, so the tip is about 6.62. The exact figure is 6.624, and 6.62 is close enough for a tip.

These shortcuts also work in reverse for a quick check. If a 15 percent tip on 36.80 comes out near 5.50, the answer is in the right range. If it comes out near 55, a decimal slipped.

Percent change versus percentage points

Percent and percentage point are two different units, and news stories mix them up often enough that it is worth learning the difference once.

The Consumer Price Index for All Urban Consumers rose 3.7 percent in the 12 months ending September 2026, while the index that leaves out food and energy rose 2.6 percent, according to the Bureau of Labor Statistics. The gap between those two figures is 1.1 percentage points. Core inflation itself moved from 2.4 percent in the year ending August to 2.6 percent in the year ending September. That is 0.2 percentage points, and it is also an 8.33 percent rise in the core rate, because 0.2 over 2.4 is 0.0833.

Use percentage points when you subtract one rate from another, and percent when you compare two quantities or divide one by the other. A savings account that goes from 4 percent to 5 percent gains one percentage point, and it pays 25 percent more interest. Both sentences describe the same change.

The index level itself was 336.940 in September 2026, and the energy index rose 20.4 percent over the same 12 months. The level means little alone; the ratio between two levels is what produces a percent change.

Successive percentages multiply instead of adding

When two percentages apply one after the other, the second one lands on a base the first one already changed. That is why the factors multiply rather than the percentages adding.

Take a 100 dollar item with 20 percent off, then another 10 percent off the reduced price. The first cut leaves 80 dollars. The second cut takes 10 percent of 80, which is 8 dollars, and leaves 72. The total discount is 28 percent, not 30, because 0.8 times 0.9 is 0.72.

The same rule explains why a 5 percent raise followed by a 5 percent pay cut does not leave you where you started. Multiply 1.05 by 0.95 and the result is 0.9975, which is a quarter of a percent below the original pay.

Discounts and taxes stack the same way. A 25 percent discount and a 7 percent tax do not cancel out, and they do not add to 18 percent off. Multiply 0.75 by 1.07 and the factor is 0.8025, so you pay 80.25 percent of the list price.

Percents in school, paychecks and official data

Percent problems show up far beyond the classroom, and the same three moves solve them: name the base, convert the percent to a decimal, then multiply or divide.

On a paycheck, a 6.2 percent Social Security deduction and a 1.45 percent Medicare deduction come off gross pay before anything else, per the Social Security Administration. On 2,400 dollars of gross pay, 6.2 percent is 148.80 and 1.45 percent is 34.80.

In official data, percents make groups of different sizes comparable. The Census Bureau put median household income at 83,730 dollars in 2024. Spending 30 percent of that on housing works out to 25,119 dollars a year, or about 2,093 dollars a month.

In school, a score of 85 percent means 85 points out of every 100 available. Two tests with different point totals are only comparable once both are turned into percents: 17 out of 20 is 85 percent and 42 out of 50 is 84 percent, close but not identical.

When a percent is used to compare groups, check what the denominator is. A rise in the percent of workers who are part time is a different claim from a rise in the number of part time workers, because the size of the workforce also moves.

Mistakes that cost points and how to catch them

Most wrong percent answers come from four habits, and each one has a quick check that catches it.

• Using the wrong starting figure. A rise from 40 to 46 is 6 / 40, which is 15 percent. Dividing by 46 gives 13.04 percent, which is the increase as a share of the new price.
• Adding percentages that apply to different bases. 20 percent off then 10 percent off is 28 percent, not 30. Multiply the factors.
• Confusing percent with percentage points. 2.4 percent to 2.6 percent is 0.2 points and an 8.33 percent rise in the rate.
• Rounding too early. Round 0.3333 to 0.33 in a long chain and the final answer drifts. Keep the full value until the last step.

One more check that catches a lot of errors: a percent of a number should be smaller than the number when the percent is under 100, and bigger when it is over 100. If 18 percent of 250 comes out at 450, a decimal moved the wrong way.

For a single rise or fall, the percent increase calculator walks through the change formula step by step. For markdowns and sale prices, the percent off calculator takes the list price and the discount. When the question is a fraction rather than a percent, the fraction to percent calculator does the division for you.

Five practice problems with answers

Work each one on paper before checking. The answer is in the second sentence.

1. A quiz has 25 questions and a student answers 21 correctly. What is the score? The score is 84 percent, and 4 missed questions are 16 percent.
2. A recipe calls for 3 cups of flour and is scaled up by 40 percent. How much flour goes in? The new amount is 4.2 cups, since 0.4 times 3 is 1.2.
3. A class of 32 pupils has 12 who walk to school. What share walks? The share is 37.5 percent, because 12 over 32 is 0.375.
4. A phone battery falls from 64 percent to 48 percent. How many points did it drop? It dropped 16 points, which is a 25 percent drop in the charge level, since 16 over 64 is 0.25.
5. A team wins 18 of its first 24 games. What is the win rate, and what rate would 30 wins in 40 games be? The first rate is 75 percent and the second is also 75 percent, so the two records are equally strong.

Words to keep straight

• Numerator: the top of a fraction, the part.
• Denominator: the bottom of a fraction, the total it is measured against.
• Hundredths: the second place after the decimal point, where a percent turns into a decimal.
• Ratio: one amount compared with another, which is what a percent is.