How to Calculate Percentages: Increase, Decrease and "Of"

Percentages express a number as a fraction of 100, and almost every percentage problem you meet is one of three questions: what is X% of Y, what percent is one number of another, and by what percentage did something change. Master those three and you can handle discounts, tips, tax, test scores, statistics and more. The Percentage Calculator answers all of them instantly, and this article explains the reasoning so you can also do them in your head.

The word "percent" literally means "per hundred," so 25% is just 25 per 100, or the fraction 0.25. Once you internalise that, converting between a percentage and a decimal, divide by 100, or move the decimal point two places, becomes second nature, and the rest follows.

Question 1: What is X% of Y?

This is the most common percentage question, finding a percentage of a number, as when working out a tip, a discount or a tax. The method is to convert the percentage to a decimal and multiply. To find 20% of 80, turn 20% into 0.2 and multiply: 0.2 × 80 = 16. That is all there is to it. A useful mental shortcut is that percentages are reversible: X% of Y always equals Y% of X, so if 20% of 80 is hard to picture, 80% of 20 gives the same 16 and may be easier.

Question 2: What percent is A of B?

Here you have two numbers and want to know what proportion one is of the other, what percent 30 is of 120, say. Divide the part by the whole and multiply by 100: 30 ÷ 120 = 0.25, times 100 is 25%. This is the question behind test scores (marks out of total), completion rates, and any "what share of the total" problem. The trap is getting the two numbers the wrong way round; the part goes on top, the whole on the bottom.

Question 3: Percentage increase and decrease

To find how much something changed in percentage terms, take the difference, divide by the original value, and multiply by 100. If a price rises from 50 to 65, the change is 15, divided by the original 50 is 0.3, or a 30% increase. A decrease works the same way with a smaller new value. The key detail is that you always divide by the original amount, not the new one, dividing by the wrong base is the most common percentage-change mistake and produces a subtly wrong answer.

Mental-maths shortcuts

A few tricks make everyday percentages quick without a calculator:

• 10%: just move the decimal one place: 10% of 240 is 24.
• 1%: move it two places: 1% of 240 is 2.4.
• 5%: half of 10%.
• 20%: double 10%.
• 15% (a common tip), 10% plus half of 10%.

Building a percentage from these round pieces, 15% as 10% plus 5%, lets you estimate tips, discounts and tax in your head almost instantly.

Where percentages show up

These three calculations underpin a huge range of everyday tasks. Discounts and sales are percentages of a price, and stacked discounts multiply rather than add, a subtlety worth understanding with a discount calculator. Tips are a percentage of a bill, handled by a tip calculator. Interest, whether on savings or loans, is percentage-based, and when it compounds over time the effect grows dramatically, as a compound interest calculator shows. In each case the underlying arithmetic is one of the three questions above.

Reversing a percentage: working backwards

One percentage skill that trips almost everyone up is working backwards from a figure that already includes a percentage. Suppose a price of $120 already includes 20% tax and you want the pre-tax amount. The instinct is to take 20% of $120 and subtract it, but that is wrong, because the 20% was added to the smaller pre-tax figure, not the larger total. The correct method is to recognise that $120 represents 120% of the original, so you divide by 1.2 to get the pre-tax $100. Taking 20% off $120 would give $96, which is not the same thing at all.

This backwards calculation appears constantly: stripping tax out of a gross price, finding the original price before a discount, or working out a starting figure from one that has grown by a known percentage. The reliable rule is always to divide by one-plus-the-percentage (as a decimal) to undo an increase, or by one-minus-the-percentage to undo a decrease. Adding or subtracting the percentage of the final figure gives a subtly wrong answer because it applies the percentage to the wrong base. This is the same trap that makes stacked discounts confusing, and it is one of the most valuable percentage insights to internalise, because getting it wrong quietly distorts prices, taxes and margins. When the numbers matter, a calculator that handles the reverse calculation removes the risk entirely, but understanding why you divide rather than subtract is what stops the mistake in the first place.

The reassuring thing about percentages is that once you recognise which of the three questions you are facing, the path to the answer is always short and always the same. There is no advanced trick to learn, only the discipline of identifying the right base to divide by and keeping percentage points separate from percentage change. Practise the mental shortcuts on everyday bills and prices and the arithmetic soon becomes automatic, with a calculator on hand for the awkward numbers and the backwards calculations that are easy to get wrong.

In summary, nearly every percentage problem is finding a percentage of a number, expressing one number as a percentage of another, or measuring a percentage change, and each is a short calculation once you treat "percent" as "divide by 100." Remember to divide by the original value for changes, keep percentage points distinct from percentages, and lean on the 10%-and-1% shortcuts for mental estimates. With those in hand, percentages stop being intimidating and become one of the most useful everyday maths skills.