Percentages are everywhere. You see them on sale signs, in exam results, on nutrition labels and in news reports about prices and wages. Yet many people feel a little unsure the moment they have to work one out without a calculator. The good news is that percentages follow a handful of simple rules, and once you understand them, most everyday problems take seconds.
In this guide we will go through what a percentage really is, how to find a percentage of an amount, how to handle increases and decreases, and the most common traps to avoid.
What a percentage actually means
The word comes from the Latin per centum, meaning "out of a hundred". So 25% simply means 25 out of every 100. That makes it easy to switch between percentages, fractions and decimals:
- 25% = 25/100 = 1/4 = 0.25
- 50% = 50/100 = 1/2 = 0.5
- 10% = 10/100 = 1/10 = 0.1
- 12.5% = 12.5/100 = 1/8 = 0.125
To turn a percentage into a decimal, divide by 100. To turn a decimal into a percentage, multiply by 100. Knowing a few of these pairs by heart makes mental maths much quicker.
Finding a percentage of an amount
The easiest mental method is to build everything from 10%. To find 10% of a number, divide it by 10. From there you can find almost anything else:
- 5% is half of 10%.
- 20% is double 10%.
- 1% is the number divided by 100.
Say you want 35% of 80. Ten per cent is 8, so 30% is 24. Five per cent is half of 8, which is 4. Add them together and you get 28. With a calculator, you can use the decimal instead: 0.35 × 80 = 28. Both methods give the same answer, and it is useful to know both so you can check one against the other.
Percentage increase and decrease
When something goes up or down by a percentage, the quickest approach is a multiplier. An increase of 20% means you end up with 120% of the original, so you multiply by 1.2. A decrease of 15% leaves you with 85%, so you multiply by 0.85.
To find the percentage change between two numbers, use this formula: change ÷ original × 100. If a value rises from 50 to 65, the change is 15. Divide 15 by 50 and you get 0.3, which is a 30% increase. Always divide by the original value, not the new one. If you want a handy list of other key rules, take a look at our page of maths formulas.
Reverse percentages
Reverse percentage questions ask you to work backwards. For example, a price is 96 after a 20% increase. What was it before? A common mistake is to take 20% of 96 and subtract it, which gives 76.8. That is wrong, because the 20% was calculated on the original price, not on 96.
The correct method is to divide by the multiplier. The new price is 120% of the original, so 96 ÷ 1.2 = 80. You can check it: 20% of 80 is 16, and 80 + 16 = 96.
Common traps to watch out for
Two mistakes catch out even confident learners. The first is assuming that an increase followed by the same decrease cancels out. If 100 goes up by 10%, it becomes 110. If 110 then goes down by 10%, it becomes 99, not 100. The second percentage is taken from a bigger number, so it removes more.
The second trap is mixing up percentages and percentage points. If an interest rate moves from 4% to 5%, it has risen by one percentage point. As a percentage change, though, it has gone up by 25%, because 1 is a quarter of 4. News reports sometimes use the two loosely, so it is worth pausing to check which one is meant.
Percentages are one of the most practical topics in maths, and a little practice goes a long way. Try working out discounts in your head next time you are shopping, then check with your phone. If numbers make you nervous, our tips on how to overcome math anxiety can help you build confidence step by step.
