A percent is a number out of 100. Percent means per hundred, so 25% means 25 out of 100, or 25100 = 0.25. To find a percent of a quantity, change the percent to a decimal and multiply: 20% of 80 is 0.20 × 80 = 16. The symbol for percent is %.
25% means 25 out of every 100. Applied to a different whole, 80, the same percent is 0.25 × 80 = 20.
Formal definition and notation
A percent is a ratio whose denominator is 100: p% means p100. So p% of a quantity W is p100 × W. A percent can be less than 1% (0.5% = 0.005) or more than 100% (150% = 1.5). Percents, decimals and fractions are three ways to write the same number: 34 = 0.75 = 75%.
Symbol
Read it as
Meaning
%
percent
out of 100: 7% = 7100
p% of W
p percent of W
p100 × W: of means multiply
100%
one hundred percent
the whole amount
Key facts
Benchmarks: 100% is the whole, 50% is half, 25% is a quarter, 10% is a tenth and 1% is a hundredth.
Decimal to percent: move the decimal point 2 places right (0.07 = 7%, 1.2 = 120%). Percent to decimal: move it 2 places left.
Fraction to percent: divide, then multiply by 100: 38 = 0.375 = 37.5%.
Mental math: 10% of a number moves its decimal point one place left, so 10% of 240 is 24 and 5% is half of that, 12.
Percents swap: 8% of 50 equals 50% of 8. Both are 4.
The percent equation
The percent equation
part = percent × whole
percent
written as a decimal or fraction: 35% = 0.35
whole
the total amount, which is 100%
part
the piece of the whole that the percent describes
Any one of the three can be the unknown. Part: 0.35 × 240 = 84. Whole: 18 ÷ 0.40 = 45. Percent: 1248 = 0.25 = 25%.
Try it: turn a fraction into a percent
Interactive
Set the numerator and denominator, or tap pieces of the bar. The readout shows the fraction as a decimal and as a percent; try fifths, fourths and eighths.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Percent examples, step by step
Example 1: Fraction to percent
Warm-up
Write 35 as a percent.
Make the denominator 100: 35 = 3 × 205 × 20 = 60100.
60 out of 100 is 60%.
Check by dividing: 3 ÷ 5 = 0.6, and 0.6 × 100 = 60.
Answer:35 = 60%.
Example 2: Percent of a number
Core
What is 35% of 240?
Change the percent to a decimal: 35% = 0.35.
Of means multiply: 0.35 × 240.
0.35 × 240 = 84. Estimate check: 35% is a bit more than a third, and a third of 240 is 80.
Answer: 35% of 240 is 84.
Example 3: Find the whole
Test-style
18 students walk to school. That is 40% of the class. How many students are in the class?
A percent describes a part of a whole: 20% of 50 is 10. Percent change compares a new value with an old one: 50 to 60 is a 20% increase.
Percentvs.Percentile
A percentile is a position in ordered data: scoring at the 90th percentile means you beat about 90% of scores, not that you got 90% of the questions right.
Quick check: 3 questions
Question 1 of 3
What is 15% of 80?
Show answer and explanation
Answer: B. 15% = 0.15 and 0.15 × 80 = 12. Choice A multiplies 15 by 80 without converting, C adds 15 to 80, and D uses 1.5 instead of 0.15.
Question 2 of 3
Which percent is equal to the decimal 0.08?
Show answer and explanation
Answer: A. Move the decimal point two places right: 0.08 = 8%. 80% is 0.8, and 0.08% and 0.8% are far smaller numbers (0.0008 and 0.008).
Question 3 of 3
12 is 30% of what number?
Show answer and explanation
Answer: C.12 = 0.30 × n, so n = 12 ÷ 0.30 = 40. Choice A finds 30% of 12 instead, B multiplies 12 by 3, and D divides 12 by 3.
Percent: frequently asked questions
Can a percent be more than 100?
Yes. 100% is the whole, so anything larger is more than the whole. 150% of 40 is 60, and a town that grows from 2,000 to 5,000 people grew by 150%. A percent of a fixed whole, like the share of a class that passed a test, cannot go over 100%, because the part cannot be bigger than the whole.
What is the difference between percent and percentage?
They mean the same idea. Percent usually follows a number, as in 25 percent or 25%. Percentage is used without a number, as in a large percentage of students or what percentage passed. In math problems you can treat the two words the same: both mean a rate out of 100.
How do you turn a fraction into a percent?
Divide the numerator by the denominator, then multiply by 100. For 720: 7 ÷ 20 = 0.35, and 0.35 × 100 = 35%. If the denominator divides 100 evenly, scale instead: 720 = 35100 = 35%. Some fractions give repeating decimals, so you round the result: 13 ≈ 33.3%.
RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Decimal PointA decimal point is the dot that separates the whole-number part of a number from its fractional part. Digits to its left are ones, tens and hundreds; digits to its right are tenths, hundredths and thousandths. In 46.25 the point sits between 6 ones and 2 tenths, and you read it aloud as “and”.Number System · Grade 4, Grade 5, Grade 6SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2Percent ChangePercent change measures how much a value grew or shrank relative to where it started: the difference divided by the original amount, written as a percent. From 50 to 60 is a 20% increase; from 80 to 60 is a 25% decrease. The original value is always the base, which is the step people get wrong.Ratios and Proportions · Grade 7, Grade 8, Algebra 1PercentileA percentile tells what percent of the values in a data set are at or below a given value. If your test score is at the 80th percentile, about 80% of the scores are at or below yours. The 25th, 50th and 75th percentiles are the first quartile, the median and the third quartile.Statistics · Grade 7, Algebra 1, StatisticsDataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6NumeratorThe numerator is the top number in a fraction. It tells how many parts are being counted, while the denominator below the fraction bar tells how many equal parts make one whole. In 35, the numerator is 3: three of five equal parts are taken.Number System · Grade 3, Grade 4, Grade 5FractionA fraction is a number that names equal parts of a whole, written ab. The bottom number, the denominator, tells how many equal parts make one whole; the top number, the numerator, tells how many of those parts you have. So 34 means 3 of 4 equal parts. Every fraction is also a point on the number line.Number System · Grade 3, Grade 4, Grade 5Unit RateA unit rate is a rate that compares a quantity to one unit of another quantity, such as 50 miles per hour or 4 dollars per notebook. To find it, divide the first quantity by the second: 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour. The word per means for each one.Ratios and Proportions · Grade 6, Grade 7, Grade 8Simple InterestSimple interest is interest paid only on the original amount of money, called the principal, at a fixed yearly rate. Find it with I = Prt: multiply the principal by the rate written as a decimal and by the time in years. The interest is the same every year, so the balance grows in a straight line.Ratios and Proportions · Grade 7, Algebra 1Percent IncreasePercent increase is how much a quantity grew, written as a percent of its original value. Subtract the original from the new value, divide by the original, and multiply by 100: from 80 to 100 is 2080 = 25%. To increase a number by r%, multiply it by 1 + r100, so 80 × 1.25 = 100.Ratios and Proportions · Grade 7, Grade 8, Algebra 1Percent DecreasePercent decrease is how much a quantity went down, written as a percent of its original value. Subtract the new value from the original, divide by the original, and multiply by 100. A price that drops from 80 dollars to 60 dollars has a decrease of 20 dollars, and 2080 = 25%.Ratios and Proportions · Grade 7, Grade 8, Algebra 1Rational NumberA rational number is any number that can be written as a fraction of two integers, ab, where b is not 0. Fractions, integers, terminating decimals, and repeating decimals are rational numbers: 34, −5 = −51, 1.6 and 0.333… all qualify. Numbers such as √2 and π are irrational.Number System · Grade 7, Grade 8, Algebra 1ProportionA proportion is an equation that says two ratios are equal, such as 12 = 36. It is read 1 is to 2 as 3 is to 6. In a true proportion the cross products are equal, which lets you find a missing value. Proportions are often used to solve scale, percent, and rate problems.Ratios and Proportions · Grade 6, Grade 7, Grade 8ProbabilityProbability measures how likely an event is, from 0 for impossible to 1 for certain. For equally likely outcomes it is the number of favorable outcomes divided by the total number of outcomes: for a fair coin, the probability of heads is 12. Probabilities can be written as fractions, decimals or percents.Probability · Grade 6, Grade 7, Grade 8