What Is a Percentage?
A percentage is a way of expressing a number as a part of one hundred. Whether you see a 20% off sale, a 72% exam score, or a bottle of juice that contains 15% of your daily vitamin C, you are looking at percentages. This guide explains exactly what they mean and how to work with them.
The meaning of per cent
The word per cent comes from the Latin phrase per centum, which means "out of one hundred". So 50 per cent simply means 50 out of 100. The symbol % is a shorthand for writing "per cent", and you will see it used everywhere from price tags to news headlines.
You can think of any percentage as answering the question: "If I split this thing into 100 equal parts, how many of those parts am I talking about?" Forty per cent is 40 of those 100 parts. One hundred per cent is all 100 parts, meaning the whole thing. Zero per cent means none of it at all.
45% visualised as a grid
Each small square is 1 out of 100. The shaded squares show 45%.
45 dark squares = 45 out of 100 = 45%
Key percentage values to remember
- 100% = the whole amount
- 75% = three quarters
- 50% = one half
- 25% = one quarter
- 10% = one tenth
- 1% = one hundredth
- 0% = nothing
Percentages and fractions
A percentage and a fraction say the same thing in different ways. Fifty per cent means 50 out of 100, which is the same as the fraction 50/100. You can simplify that fraction to 1/2, which is why 50% means a half.
To convert any fraction to a percentage, divide the top number (numerator) by the bottom number (denominator) and then multiply by 100.
To go the other way and convert a percentage to a fraction, write it over 100 and simplify. For example, 40% = 40/100 = 2/5.
Percentages and decimals
Percentages and decimals are closely linked. To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100.
This decimal connection is very useful for calculations. To find 35% of 200, you can work out 0.35 × 200 = 70. This is the standard multiplier method used throughout GCSE maths.
Percentages in everyday life
Percentages appear in almost every area of daily life. Here are some of the most common places you will encounter them.
Shopping discounts
"20% off" means the shop removes 20 out of every 100p from the price. A £50 jacket with 20% off saves you £10, so you pay £40. The Discount Calculator can work this out for you instantly.
VAT (Value Added Tax)
In the UK, most goods and services have 20% VAT added to the price. This means you pay the original price plus an extra 20% on top. A plumber who quotes £100 plus VAT will charge you £120 in total. The VAT Calculator handles this in one step.
Exam and test scores
If you score 36 out of 50 on a test, your percentage is 36 ÷ 50 × 100 = 72%. Expressing scores as percentages makes it easy to compare results across tests that have different totals.
Nutrition labels
Food packaging often shows what percentage of your recommended daily allowance (RDA) a serving contains. "15% of your daily calcium" means one serving provides 15 out of the 100 parts that make up a full daily intake.
Savings and interest
Banks pay interest on savings as a percentage. An interest rate of 3% per year means for every £100 you save, you earn £3 over the year. Over multiple years, this builds up through compound interest.
News and statistics
You will regularly see statements such as "unemployment fell by 0.3 percentage points" or "house prices rose 7% this year". Understanding percentages helps you make sense of numbers in the news and avoid being misled by statistics.
Try the calculators
Now that you understand what a percentage is, these free calculators will help you work them out quickly.
Percentage of a Number Calculator
Find what 20% of 150 is, or any other percentage of any number.
Fraction to Percentage Calculator
Convert any fraction to a percentage with step-by-step workings.
Percentage to Decimal Calculator
Convert any percentage to its decimal equivalent instantly.
Discount Calculator
Calculate sale prices and savings from any discount percentage.
VAT Calculator
Add or remove UK VAT from any amount in seconds.
History of percentages
The idea of expressing quantities as fractions of one hundred is far older than the % symbol itself.
Ancient Rome
Roman merchants and tax collectors regularly worked with fractions that had a denominator of 100, even without a dedicated symbol for them. Emperor Augustus famously levied a tax of 1/100 on goods sold at auction, a rate recognisable to any modern reader as 1%. The Romans found hundredths particularly useful for financial calculations because they divided their basic monetary unit, the as, into 100 parts.
The Middle Ages
As trade expanded across Europe in the medieval period, calculations with a denominator of 100 became increasingly standardised. Italian merchants, who dominated European finance during this era, began writing interest rates and commercial fractions as "per cento" in their account books. This made comparison between different contracts much easier, since everything was expressed on the same scale of one hundred.
The 17th century
By the 1600s, interest rates across Europe were routinely quoted in hundredths. Financial manuals of the period instructed readers to think in terms of "per cent per annum", and the phrase was appearing regularly in English texts on arithmetic and commerce. The groundwork was being laid for a truly universal notation.
The % symbol
The % symbol emerged from the gradual contraction of the Italian "per cento" in handwritten manuscripts. Writers began dropping "per" and compressing "cento" (one hundred) into a shorthand of two small circles with a line between them. Early examples appear in Italian commercial manuscripts from the 15th century. The symbol slowly spread to other European countries through trade documents and printed arithmetic texts, eventually becoming the universal standard we use today.
Related resources
Percentage of a Number Calculator
Work out any percentage of any amount instantly.
Fraction to Percentage Calculator
Convert any fraction to a percentage in one step.
KS2 Practice Questions
30 practice questions for years 5 and 6 with worked answers.
Very Easy Percentage Worksheet
A gentle printable introduction to percentages for beginners.
Year 6 Percentage Worksheet
Printable worksheet covering 50%, 25%, 10% and amounts for year 6.